SOLUTION: 3x^2-11x-2=0

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Question 82167:
3x^2-11x-2=0
Answer by jim_thompson5910(35256) 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 3x%5E2%2B-11x%2B-2+=+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=%28-11%29%5E2-4%2A3%2A-2=145.

Discriminant d=145 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--11%2B-sqrt%28+145+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-11%29%2Bsqrt%28+145+%29%29%2F2%5C3+=+3.84026576313205
x%5B2%5D+=+%28-%28-11%29-sqrt%28+145+%29%29%2F2%5C3+=+-0.173599096465383

Quadratic expression 3x%5E2%2B-11x%2B-2 can be factored:
3x%5E2%2B-11x%2B-2+=+3%28x-3.84026576313205%29%2A%28x--0.173599096465383%29
Again, the answer is: 3.84026576313205, -0.173599096465383. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-11%2Ax%2B-2+%29