jmc

The horizontal asymptote is the horizontal line that $f$ approaches as $x\to \pm \infty$. Since the degree of the denominator is greater than the degree of the numerator, it follows that the horizontal asymptote occurs at the line $y=0$. Setting this equal to $f(x)$, $$\frac{2x-6}{x^3-7x^2-2x+6}⟹2x-6=0.$$Thus, $x=\boxed{3}$.