document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=402215>Question 402215</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the correct set up for this problem and how do I arrive at answer of a = -1/3.\r<BR>\n" );
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document.write( "5a + 1/4a + 6 = 3/4\r<BR>\n" );
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document.write( "I figured the LCD to be 2(2a + 3)\r<BR>\n" );
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document.write( "2(2a + 3)* 5a + 1/2(2a + 3) = 2(2a + 3)*3/4\r<BR>\n" );
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document.write( "= 5a + 1 = 2a + 3 * 3/2 (This is where I am having problem in solving this problem. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #284542 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=284542\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5a + 1/(4a+6) = 3/4<BR>\n" );
document.write( "5a + 1/(2(2a+3)) = 3/4<BR>\n" );
document.write( "multiply both sides by 4(2a+3) <BR>\n" );
document.write( "5a(4(2a+3)) + 2 = 3(2a+3)<BR>\n" );
document.write( "5a(8a+12) + 2 = 3(2a+3)<BR>\n" );
document.write( "40a^2+60a + 2 = 6a+9<BR>\n" );
document.write( "40a^2+54a + 2 = 9<BR>\n" );
document.write( "40a^2+54a-7 = 0<BR>\n" );
document.write( "apply the \"quadratic formula\" to get:<BR>\n" );
document.write( "a = {0.119, -1.469}<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Details of quadratic:<BR>\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=aa%5E2%2Bba%2Bc=0 ALIGN=MIDDLE  ALT=\"aa%5E2%2Bba%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40a%5E2%2B54a%2B-7+=+0 ALIGN=MIDDLE  ALT=\"40a%5E2%2B54a%2B-7+=+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=a%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"a%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=%2854%29%5E2-4%2A40%2A-7=4036 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2854%29%5E2-4%2A40%2A-7=4036\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=4036 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+=+%28-54%2B-sqrt%28+4036+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-54%2B-sqrt%28+4036+%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=a%5B1%5D+=+%28-%2854%29%2Bsqrt%28+4036+%29%29%2F2%5C40+=+0.11911900871343 ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+%28-%2854%29%2Bsqrt%28+4036+%29%29%2F2%5C40+=+0.11911900871343\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D+=+%28-%2854%29-sqrt%28+4036+%29%29%2F2%5C40+=+-1.46911900871343 ALIGN=MIDDLE  ALT=\"a%5B2%5D+=+%28-%2854%29-sqrt%28+4036+%29%29%2F2%5C40+=+-1.46911900871343\"   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=40a%5E2%2B54a%2B-7 ALIGN=MIDDLE  ALT=\"40a%5E2%2B54a%2B-7\"   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=40a%5E2%2B54a%2B-7+=+40%28a-0.11911900871343%29%2A%28a--1.46911900871343%29 ALIGN=MIDDLE  ALT=\"40a%5E2%2B54a%2B-7+=+40%28a-0.11911900871343%29%2A%28a--1.46911900871343%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.11911900871343, -1.46911900871343.\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+40%2Ax%5E2%2B54%2Ax%2B-7+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+40%2Ax%5E2%2B54%2Ax%2B-7+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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