SOLUTION: Solve the equation x+ 3x^2-18x-40=0

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Question 1133827: Solve the equation x+ 3x^2-18x-40=0
Answer by Alan3354(69443) About Me  (Show Source):
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Solve the equation x+ 3x^2-18x-40=0
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3x^2-17x-40=0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-17x%2B-40+=+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=%28-17%29%5E2-4%2A3%2A-40=769.

Discriminant d=769 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--17%2B-sqrt%28+769+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-17%29%2Bsqrt%28+769+%29%29%2F2%5C3+=+7.45514154128735
x%5B2%5D+=+%28-%28-17%29-sqrt%28+769+%29%29%2F2%5C3+=+-1.78847487462068

Quadratic expression 3x%5E2%2B-17x%2B-40 can be factored:
3x%5E2%2B-17x%2B-40+=+%28x-7.45514154128735%29%2A%28x--1.78847487462068%29
Again, the answer is: 7.45514154128735, -1.78847487462068. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-17%2Ax%2B-40+%29