SOLUTION: Please help me solve the equation: {{{ x+5/7x=8/13/(-7)}}}

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Question 246130: Please help me solve the equation: +x%2B5%2F7x=8%2F13%2F%28-7%29
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x%2B5%2F7x=8%2F13%2F%28-7%29
%287x%5E2+%2B+5%29%2F7x+=+8%2F%28-91%29
-91%2A%287x%5E2+%2B+5%29+=+56x
-91x%5E2+%2B+65+=+8x
91x%5E2+%2B+8x+-+65+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 91x%5E2%2B8x%2B-65+=+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=%288%29%5E2-4%2A91%2A-65=23724.

Discriminant d=23724 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+23724+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+23724+%29%29%2F2%5C91+=+0.802340504592974
x%5B2%5D+=+%28-%288%29-sqrt%28+23724+%29%29%2F2%5C91+=+-0.890252592505062

Quadratic expression 91x%5E2%2B8x%2B-65 can be factored:
91x%5E2%2B8x%2B-65+=+%28x-0.802340504592974%29%2A%28x--0.890252592505062%29
Again, the answer is: 0.802340504592974, -0.890252592505062. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+91%2Ax%5E2%2B8%2Ax%2B-65+%29