Answer
(-$\infty$,-3) $\cup$ (6,$\infty$)
Work Step by Step
$x^{2}$ $\gt$ 3(x+6)
$x^{2}$ $\gt$ 3x+18
$x^{2}$ -3x -18 $\gt$ 0
(x-6)(x+3) $\gt$ 0
From factored trinomial we can see that factors are zero
when x=-3 or x=6, endpoints don't satisfy the inequality.
Plug values from intervals to decide which of them satisfy the inequality.