document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132299>Question 132299</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Someone please help.\r<BR>\n" );
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document.write( "y^2=5/7y+3/7  Does it have 2 non-real solutions, 2 real solutions, or 1 real solutions.\r<BR>\n" );
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document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #96655 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=96655\">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=y%5E2=%285%2F7%29y%2B3%2F7 ALIGN=MIDDLE  ALT=\"y%5E2=%285%2F7%29y%2B3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%285%2F7%29y%2B3%2F7-y%5E2 ALIGN=MIDDLE  ALT=\"0=%285%2F7%29y%2B3%2F7-y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-y%5E2%2B%285%2F7%29y%2B3%2F7 ALIGN=MIDDLE  ALT=\"0=-y%5E2%2B%285%2F7%29y%2B3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2A0=7%28-y%5E2%2B%285%2F7%29y%2B3%2F7%29 ALIGN=MIDDLE  ALT=\"7%2A0=7%28-y%5E2%2B%285%2F7%29y%2B3%2F7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD 7. This will eliminate the fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-7y%5E2%2B5y%2B3 ALIGN=MIDDLE  ALT=\"0=-7y%5E2%2B5y%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply\r<BR>\n" );
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document.write( "From the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the discriminant consists of all of the terms in the square root. So the discriminant is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=b%5E2-4ac ALIGN=MIDDLE  ALT=\"D=b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the discriminant tells us how many solutions (and what type of solutions) we can expect for any quadratic.\r<BR>\n" );
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document.write( "Now let's find the discriminant for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-7y%5E2%2B5y%2B3 ALIGN=MIDDLE  ALT=\"y=-7y%5E2%2B5y%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=b%5E2-4ac ALIGN=MIDDLE  ALT=\"D=b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=%285%29%5E2-4%2A-7%2A3 ALIGN=MIDDLE  ALT=\"D=%285%29%5E2-4%2A-7%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-7, b=5, c=3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=25-4%2A-7%2A3 ALIGN=MIDDLE  ALT=\"D=25-4%2A-7%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 5 to get 25\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=25%2B84 ALIGN=MIDDLE  ALT=\"D=25%2B84\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -4*-7*3 to get 84\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=109 ALIGN=MIDDLE  ALT=\"D=109\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine 25 and 84 to get 109\r<BR>\n" );
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document.write( "Since the discriminant equals 109  (which is greater than zero) , this means  there are two real solutions. Remember if the discriminant is greater than zero, then the quadratic will have two real solutions.\r<BR>\n" );
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