SOLUTION: 14x^2-27x-20=0

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Question 344726: 14x^2-27x-20=0
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Hi
14x%5E%282%29-27x-20=0
Using the Quadratic Formula to solve:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 14x%5E2%2B-27x%2B-20+=+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=%28-27%29%5E2-4%2A14%2A-20=1849.

Discriminant d=1849 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--27%2B-sqrt%28+1849+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-27%29%2Bsqrt%28+1849+%29%29%2F2%5C14+=+2.5
x%5B2%5D+=+%28-%28-27%29-sqrt%28+1849+%29%29%2F2%5C14+=+-0.571428571428571

Quadratic expression 14x%5E2%2B-27x%2B-20 can be factored:
14x%5E2%2B-27x%2B-20+=+14%28x-2.5%29%2A%28x--0.571428571428571%29
Again, the answer is: 2.5, -0.571428571428571. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+14%2Ax%5E2%2B-27%2Ax%2B-20+%29