Answer
$$x=2\sqrt{7},\:x=-2\sqrt{7}$$
Work Step by Step
Solving by setting the expressions equal to each other and then using the quadratic formula, we find:
$$ x\left(x-5\right)+5\left(x-5\right)=\frac{3}{x-5}\left(x-5\right) \\ x\left(x-5\right)+5\left(x-5\right)=3\\ x^2-28=0\\ x_{1,\:2}=\frac{-0\pm \sqrt{0^2-4\cdot \:1\left(-28\right)}}{2\cdot \:1}\\ x=2\sqrt{7},\:x=-2\sqrt{7}$$
