SOLUTION: 5x-3 (x-4) = 6x+4

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Question 344108: 5x-3 (x-4) = 6x+4
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
%285x-3%29%28x-4%29=6x%2B4
5x%5E2-3x-20x%2B12=6x%2B4
5x%5E2-29x%2B9=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-29x%2B9+=+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=%28-29%29%5E2-4%2A5%2A9=661.

Discriminant d=661 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--29%2B-sqrt%28+661+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-29%29%2Bsqrt%28+661+%29%29%2F2%5C5+=+5.47099202643649
x%5B2%5D+=+%28-%28-29%29-sqrt%28+661+%29%29%2F2%5C5+=+0.329007973563512

Quadratic expression 5x%5E2%2B-29x%2B9 can be factored:
5x%5E2%2B-29x%2B9+=+5%28x-5.47099202643649%29%2A%28x-0.329007973563512%29
Again, the answer is: 5.47099202643649, 0.329007973563512. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-29%2Ax%2B9+%29