document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=541888>Question 541888</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This operation is tough for me, I think I may know but it would help out greatly if I was shown how it works. Thank you\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28%281%2F%285x%29%29+-%282%2F%285x%29%29%29+%2B+6+=+%281%2F6%29%283x-2%29 ALIGN=MIDDLE  ALT=\"3%28%281%2F%285x%29%29+-%282%2F%285x%29%29%29+%2B+6+=+%281%2F6%29%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Also if you could show how it is checked\r<BR>\n" );
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document.write( "Thanks again. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #356051 by </B><A HREF=/tutors/aboutme.mpl?userid=JBarnum><B>JBarnum(2146)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JBarnum><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=JBarnum><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=356051\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28%281%2F%285x%29%29+-%282%2F%285x%29%29%29+%2B+6+=+%281%2F6%29%283x-2%29 ALIGN=MIDDLE  ALT=\"3%28%281%2F%285x%29%29+-%282%2F%285x%29%29%29+%2B+6+=+%281%2F6%29%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28-%281%2F%285x%29%29%29+%2B+6+=+%281%2F6%29%283x-2%29 ALIGN=MIDDLE  ALT=\"3%28-%281%2F%285x%29%29%29+%2B+6+=+%281%2F6%29%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F%285x%29+%2B+6+=+%281%2F6%29%283x-2%29 ALIGN=MIDDLE  ALT=\"-3%2F%285x%29+%2B+6+=+%281%2F6%29%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > multiply everything by the common denom (5x*6)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%2A6%29%2A%28-3%2F%285x%29%29+%2B+%285x%2A6%29%2A6+=+%281%2F6%29%285x%2A6%29%283x-2%29 ALIGN=MIDDLE  ALT=\"%285x%2A6%29%2A%28-3%2F%285x%29%29+%2B+%285x%2A6%29%2A6+=+%281%2F6%29%285x%2A6%29%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > do cancelations<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%285x%29%2A6%29%2A%28-3%2Fcross%285x%29%29+%2B+%285x%2A6%29%2A6+=+%281%2Fcross%286%29%29%285x%2Across%286%29%29%283x-2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-18+%2B+180x+=+15x%5E2-10x%29 ALIGN=MIDDLE  ALT=\"-18+%2B+180x+=+15x%5E2-10x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-18+%2B+180x+=+15x%5E2-10x%29 ALIGN=MIDDLE  ALT=\"-18+%2B+180x+=+15x%5E2-10x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > subtract 180x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-18+=+15x%5E2-190x%29 ALIGN=MIDDLE  ALT=\"-18+=+15x%5E2-190x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >add 18<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+15x%5E2-190x%2B18%29 ALIGN=MIDDLE  ALT=\"0+=+15x%5E2-190x%2B18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "quadratic formula<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%5E2%2B-190x%2B18+=+0 ALIGN=MIDDLE  ALT=\"15x%5E2%2B-190x%2B18+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-190%29%5E2-4%2A15%2A18=35020 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-190%29%5E2-4%2A15%2A18=35020\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=35020 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--190%2B-sqrt%28+35020+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--190%2B-sqrt%28+35020+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-190%29%2Bsqrt%28+35020+%29%29%2F2%5C15+=+12.5712104651075 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-190%29%2Bsqrt%28+35020+%29%29%2F2%5C15+=+12.5712104651075\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-190%29-sqrt%28+35020+%29%29%2F2%5C15+=+0.0954562015591658 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-190%29-sqrt%28+35020+%29%29%2F2%5C15+=+0.0954562015591658\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%5E2%2B-190x%2B18 ALIGN=MIDDLE  ALT=\"15x%5E2%2B-190x%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x%5E2%2B-190x%2B18+=+15%28x-12.5712104651075%29%2A%28x-0.0954562015591658%29 ALIGN=MIDDLE  ALT=\"15x%5E2%2B-190x%2B18+=+15%28x-12.5712104651075%29%2A%28x-0.0954562015591658%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 12.5712104651075, 0.0954562015591658.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+15%2Ax%5E2%2B-190%2Ax%2B18+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+15%2Ax%5E2%2B-190%2Ax%2B18+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "x=12.5712 , 0.0954<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28%281%2F%285x%29%29+-%282%2F%285x%29%29%29+%2B+6+=+%281%2F6%29%283x-2%29 ALIGN=MIDDLE  ALT=\"3%28%281%2F%285x%29%29+-%282%2F%285x%29%29%29+%2B+6+=+%281%2F6%29%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28%281%2F%285%280.0954%29%29%29+-%282%2F%285%280.0954%29%29%29%29+%2B+6+=+%281%2F6%29%283%280.0954%29-2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28%281%2F.477%29-%282%2F.477%29%29+%2B+6+=+%281%2F6%29%28.2862-2%29 ALIGN=MIDDLE  ALT=\"3%28%281%2F.477%29-%282%2F.477%29%29+%2B+6+=+%281%2F6%29%28.2862-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28-1%2F.477%29+%2B+6+=+%281%2F6%29%28-1.7138%29 ALIGN=MIDDLE  ALT=\"3%28-1%2F.477%29+%2B+6+=+%281%2F6%29%28-1.7138%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%2F.477%29+%2B+6+=+%28-.2856%29 ALIGN=MIDDLE  ALT=\"%28-3%2F.477%29+%2B+6+=+%28-.2856%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6.28+%2B+6+=+-.28 ALIGN=MIDDLE  ALT=\"-6.28+%2B+6+=+-.28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-.28=-.28 ALIGN=MIDDLE  ALT=\"-.28=-.28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "correct<BR>\n" );
document.write( "you would do same with other x value to check\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );