SOLUTION: Solve using the quadratic formula. 3 = 11x - 6x(squared)

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Question 229171: Solve using the quadratic formula.
3 = 11x - 6x(squared)

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve using the quadratic formula.
3 = 11x - 6x(squared)
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-6x%5E2+%2B+11x+-+3+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -6x%5E2%2B11x%2B-3+=+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%2A-6%2A-3=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-11%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2811%29%2Bsqrt%28+49+%29%29%2F2%5C-6+=+0.333333333333333
x%5B2%5D+=+%28-%2811%29-sqrt%28+49+%29%29%2F2%5C-6+=+1.5

Quadratic expression -6x%5E2%2B11x%2B-3 can be factored:
-6x%5E2%2B11x%2B-3+=+%28x-0.333333333333333%29%2A%28x-1.5%29
Again, the answer is: 0.333333333333333, 1.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-6%2Ax%5E2%2B11%2Ax%2B-3+%29