SOLUTION: Solve 2a2 + 11a− 6 = 0 using the quadratic formula

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Question 522809: Solve 2a2 + 11a− 6 = 0 using the quadratic formula
Answer by Maths68(1474) About Me  (Show Source):
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2a%5E2%2B11a-6=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B11x%2B-6+=+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=%2811%29%5E2-4%2A2%2A-6=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-11%2B-sqrt%28+169+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2811%29%2Bsqrt%28+169+%29%29%2F2%5C2+=+0.5
x%5B2%5D+=+%28-%2811%29-sqrt%28+169+%29%29%2F2%5C2+=+-6

Quadratic expression 2x%5E2%2B11x%2B-6 can be factored:
2x%5E2%2B11x%2B-6+=+2%28x-0.5%29%2A%28x--6%29
Again, the answer is: 0.5, -6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B11%2Ax%2B-6+%29