Algebra

First, we want to get rid of the nasty fractions. 

Let's do this by multiplying both sides by the LCM of the denominators. 

By doing this, we have

$10\left(x+4\right)=5\left(x-3\right)\left(x+5\right)+2\left(x+7\right)\left(x+5\right)$

Distributing every number in and moving all terms to one side, we have

$7x^{2}+24x-45=0$

Using the quadratic equation and finding what x is, we have

$x=\frac{3\sqrt{51}-12}{7}\\ x=\frac{-3\sqrt{51}-12}{7}$

Thanks! :)