Algebra

First, we want to get rid of the deniminators. We can do this by multiplying both sides by the LCM of the denominators. 

The LCM is (x-5)(x-2). 

We have

$x\left(x-2\right)=2\left(x-5\right)+2x\left(x-5\right)\left(x-2\right)$

We now get a quadratic. 

We get 

$x^2-2x=2x^3-14x^2+22x-10\\ 2x^3-15x^2+24x-10=0$

This where it gets tricky. There are no integer roots for this equation. 

We could use the Newton-Raphson equation, and we eventually get

$x\approx \:0.67798\dots ,\:x\approx \:1.34697\dots ,\:x\approx \:5.47503\dots$

I hope this was clear enough!

Thanks! :)