Answer
$\{6\}$
Work Step by Step
The LHS is nonnegative, so the RHS = x is also nonnegative.
(We will exclude any negative solution)
$\sqrt{3x+18}=x \quad $... Square both sides
$3x+18=x^{2}$
$ x^{2}-3x-18=0$
We factor this trinomial by finding two factors of $-18$ that add to $-3$; they are $+3$ and $-6$.
$(x+3)(x-6)=0$
$ x=-3,\quad x=-6$
$ x=-3 $ is extraneous (x must be nonnegative), so we discard it.
$ x=6$ is a valid solution
Check:
$\sqrt{3(6)+18}=6$
$ \sqrt{18+18}=6$
$\sqrt{36}=6$
The solution set is $\{6\}$.
