SOLUTION: I have tried many different ways to solve this equation and I just can't seem to get it right: 5/3x-8=x/x+2 I know I have to cross multiply but when I d

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Question 634967: I have tried many different ways to solve this equation and I just can't seem to get it right:
5/3x-8=x/x+2
I know I have to cross multiply but when I do that I end up with this:

5x+10=3x^2-8x
I don't really know where to go from there. If I add 8x to 5x then it seems like that's all the simplifying I can do, unless I subtract 3x^2 and somehow turn it into a quadratic formula, but that also doesn't seem right. I also tried to see if I could just cross out the x's on x/x+2 but then that would leave me with 0/2 (simply just a zero) and then I would just have 5/3x-8. Where would I go from there? And I don't think that the answer is still supposed to have variables, I think that it is a number, but I just don't see how that is possible. Please help! Thank you so much.


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I have tried many different ways to solve this equation and I just can't seem to get it right:
5/3x-8=x/x+2
==================
If you mean
5/(3x-8) = x/(x+2)
Cross multiply
5(x+2) = x(3x-8)
5x%2B10+=+3x%5E2+-+8x
3x%5E2+-+13x+-+10+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-13x%2B-10+=+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=%28-13%29%5E2-4%2A3%2A-10=289.

Discriminant d=289 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--13%2B-sqrt%28+289+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+289+%29%29%2F2%5C3+=+5
x%5B2%5D+=+%28-%28-13%29-sqrt%28+289+%29%29%2F2%5C3+=+-0.666666666666667

Quadratic expression 3x%5E2%2B-13x%2B-10 can be factored:
3x%5E2%2B-13x%2B-10+=+%28x-5%29%2A%28x--0.666666666666667%29
Again, the answer is: 5, -0.666666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-13%2Ax%2B-10+%29

=================
Does that work?