jmc

Subtracting $2x$ from both sides, it follows that $x^2-2x-15<0$. This factors as $x^2-2x-15=(x-5)(x+3)<0$, from which it follows (by testing values or inspection) that $-3<x<5$. Then $a=-2,b=4$, and $b-a$ is $4-(-2)=\boxed{6}$.