Answer
$x=9$
Work Step by Step
Squaring both sides of the given equation, $
\sqrt{3x+9}=6
,$ then the solution/s is/are
\begin{array}{l}\require{cancel}
3x+9=36
\\\\
3x=36-9
\\\\
3x=27
\\\\
x=\dfrac{27}{3}
\\\\
x=9
.\end{array}
Upon checking, $
x=9
$ satisfies the original equation.