Answer
$\frac{5}{2}$, $4$
Work Step by Step
Step 1. Multiply $x(x^2+10)$ on both sides to get $13x = 2x^2+20\longrightarrow 2x^2-13x+20=0$
Step 2. Factor the equation to get $(2x-5)(x-4)=0$, thus $x=\frac{5}{2}$ and $x=4$
Step 3. Check the answers and they both fit.