document.write( "Question 168794: How would you solve the following equation by using the quadratic formula? \r
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\n" ); document.write( "\n" ); document.write( "\"3%2F4x%5E2=1%2F2x%2B1%2F3\"\r
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Algebra.Com's Answer #124441 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
\"3%2F4x%5E2=1%2F2x%2B1%2F3\"
\n" ); document.write( "Multiply both sides by 12x^2 to get:
\n" ); document.write( "\"9=6x%2B4x%5E2\"
\n" ); document.write( "\"9=4x%5E2%2B6x\"
\n" ); document.write( "\"0=4x%5E2%2B6x-9\"
\n" ); document.write( "Now, you can apply your quadratic equation to get the solution of:
\n" ); document.write( "x ={0.927, -2.427}
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\n" ); document.write( "Details below:
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"4x%5E2%2B6x%2B-9+=+0\") has the following solutons:
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\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%286%29%5E2-4%2A4%2A-9=180\".
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\n" ); document.write( " Discriminant d=180 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28-6%2B-sqrt%28+180+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%286%29%2Bsqrt%28+180+%29%29%2F2%5C4+=+0.927050983124842\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%286%29-sqrt%28+180+%29%29%2F2%5C4+=+-2.42705098312484\"
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\n" ); document.write( " Quadratic expression \"4x%5E2%2B6x%2B-9\" can be factored:
\n" ); document.write( " \"4x%5E2%2B6x%2B-9+=+4%28x-0.927050983124842%29%2A%28x--2.42705098312484%29\"
\n" ); document.write( " Again, the answer is: 0.927050983124842, -2.42705098312484.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B6%2Ax%2B-9+%29\"
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