SOLUTION: 7x^2-3x-5=0

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Question 637867: 7x^2-3x-5=0
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 7x%5E2%2B-3x%2B-5+=+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=%28-3%29%5E2-4%2A7%2A-5=149.

Discriminant d=149 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+149+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+149+%29%29%2F2%5C7+=+1.08618254398098
x%5B2%5D+=+%28-%28-3%29-sqrt%28+149+%29%29%2F2%5C7+=+-0.65761111540955

Quadratic expression 7x%5E2%2B-3x%2B-5 can be factored:
7x%5E2%2B-3x%2B-5+=+7%28x-1.08618254398098%29%2A%28x--0.65761111540955%29
Again, the answer is: 1.08618254398098, -0.65761111540955. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+7%2Ax%5E2%2B-3%2Ax%2B-5+%29