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

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) (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)

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=289 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 5, -0.666666666666667. Here's your graph:

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

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