Answer
$\{2\}$
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
$20-8x=x^{2}$
$ x^{2}+8x-20=0$
We factor this trinomial by finding two factors of $-20$ that add to $+8$; they are $+10$ and $-2$.
$(x+10)(x-2)=0$
$ x=-10,\quad x=2$
$ x=-10 $ is extraneous (x must be nonnegative), so we discard it.
$ x=2$ is a valid solution
Check:
$\sqrt{20-8(2)}=2$
$ \sqrt{20-16}=2$
$\sqrt{4}=2$
The solution set is $\{2\}$.
