document.write( "Question 253097: What are the solutions of: x=15x^2-6? \n" ); document.write( "

Algebra.Com's Answer #185316 by Alan3354(69443) $\"\"$ $\"About$

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What are the solutions of: x=15x^2-6
\n" ); document.write( "15x^2 - x - 6 = 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"15x%5E2%2B-1x%2B-6+=+0\"$ ) 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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%28-1%29%5E2-4%2A15%2A-6=361\"$ .
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\n" ); document.write( " Discriminant d=361 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28--1%2B-sqrt%28+361+%29%29%2F2%5Ca\"$ .
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\n" ); document.write( " $\"x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+361+%29%29%2F2%5C15+=+0.666666666666667\"$
\n" ); document.write( " $\"x%5B2%5D+=+%28-%28-1%29-sqrt%28+361+%29%29%2F2%5C15+=+-0.6\"$
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\n" ); document.write( " Quadratic expression $\"15x%5E2%2B-1x%2B-6\"$ can be factored:
\n" ); document.write( " $\"15x%5E2%2B-1x%2B-6+=+%28x-0.666666666666667%29%2A%28x--0.6%29\"$
\n" ); document.write( " Again, the answer is: 0.666666666666667, -0.6.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+15%2Ax%5E2%2B-1%2Ax%2B-6+%29\"$

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