SOLUTION: 2x^2-1 = 5x

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Question 22368: 2x^2-1 = 5x
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Subtract "5x" from each side of the equation to get:
2x^2-5x-1=0
Use the quadratic formula to find "x".
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-5x%2B-1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-5%29%5E2-4%2A2%2A-1=33.

Discriminant d=33 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+33+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+33+%29%29%2F2%5C2+=+2.68614066163451
x%5B2%5D+=+%28-%28-5%29-sqrt%28+33+%29%29%2F2%5C2+=+-0.186140661634507

Quadratic expression 2x%5E2%2B-5x%2B-1 can be factored:
2x%5E2%2B-5x%2B-1+=+2%28x-2.68614066163451%29%2A%28x--0.186140661634507%29
Again, the answer is: 2.68614066163451, -0.186140661634507. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-5%2Ax%2B-1+%29

Cheers,
Stan H.