SOLUTION: 5x^2-2x-3=15.find x

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Question 762610: 5x^2-2x-3=15.find x
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
a=5, b=-2, c=-18


Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-2x%2B-18+=+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=%28-2%29%5E2-4%2A5%2A-18=364.

Discriminant d=364 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+364+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+364+%29%29%2F2%5C5+=+2.10787840283389
x%5B2%5D+=+%28-%28-2%29-sqrt%28+364+%29%29%2F2%5C5+=+-1.70787840283389

Quadratic expression 5x%5E2%2B-2x%2B-18 can be factored:
5x%5E2%2B-2x%2B-18+=+5%28x-2.10787840283389%29%2A%28x--1.70787840283389%29
Again, the answer is: 2.10787840283389, -1.70787840283389. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-2%2Ax%2B-18+%29