SOLUTION: How can one find the solutions of the quadratic equation by using the quadratic formula method? State the formula

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Question 463598: How can one find the solutions of the quadratic equation by using the quadratic formula method?
State the formula

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
For example, 2x%5E2+%2B+5x+-+7+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B5x%2B-7+=+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=%285%29%5E2-4%2A2%2A-7=81.

Discriminant d=81 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+81+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+81+%29%29%2F2%5C2+=+1
x%5B2%5D+=+%28-%285%29-sqrt%28+81+%29%29%2F2%5C2+=+-3.5

Quadratic expression 2x%5E2%2B5x%2B-7 can be factored:
2x%5E2%2B5x%2B-7+=+%28x-1%29%2A%28x--3.5%29
Again, the answer is: 1, -3.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B5%2Ax%2B-7+%29