SOLUTION: Solve by using the quadratic formula. 4/w^2-11/w+6=0

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Question 903003: Solve by using the quadratic formula.
4/w^2-11/w+6=0
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
4/w^2*w^2-11w*w^2/w^2+6w^2=0
4-11w+6w^2=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B-11x%2B4+=+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%2A6%2A4=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--11%2B-sqrt%28+25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-11%29%2Bsqrt%28+25+%29%29%2F2%5C6+=+1.33333333333333
x%5B2%5D+=+%28-%28-11%29-sqrt%28+25+%29%29%2F2%5C6+=+0.5

Quadratic expression 6x%5E2%2B-11x%2B4 can be factored:
6x%5E2%2B-11x%2B4+=+6%28x-1.33333333333333%29%2A%28x-0.5%29
Again, the answer is: 1.33333333333333, 0.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-11%2Ax%2B4+%29