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

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Question 632509: 3x^2-3x-2=0
Found 2 solutions by stanbon, richwmiller:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
3x^2-3x-2=0
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x = [3 +- sqrt(9-4*3*-2)]/6
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x = [3 +- sqrt(33)]/6
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x = (1/2) + (1/6)sqrt(33) or x = (1/2) - (1/6)sqrt(33)
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Cheers,
Stan H.

Answer by richwmiller(17219) 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-3x%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=%28-3%29%5E2-4%2A3%2A-2=33.

Discriminant d=33 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+33+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+33+%29%29%2F2%5C3+=+1.45742710775634
x%5B2%5D+=+%28-%28-3%29-sqrt%28+33+%29%29%2F2%5C3+=+-0.457427107756338

Quadratic expression 3x%5E2%2B-3x%2B-2 can be factored:
3x%5E2%2B-3x%2B-2+=+3%28x-1.45742710775634%29%2A%28x--0.457427107756338%29
Again, the answer is: 1.45742710775634, -0.457427107756338. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-3%2Ax%2B-2+%29