#### Answer

$x=45$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\sqrt{3x+9}=12
,$ raise both sides to the exponent equal to the index of the radical. Then use the properties of equality to isolate the variable. Finally, do checking of the solution/s with the original equation.
$\bf{\text{Solution Details:}}$
Get rid of the radical symbol by raising both sides of the equation above to the exponent equal to $
2
$ (the same index as the radical). This results to
\begin{array}{l}\require{cancel}
(\sqrt{3x+9})^2=12^2
\\\\
3x+9=144
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
3x=144-9
\\\\
3x=135
\\\\
x=\dfrac{135}{3}
\\\\
x=45
.\end{array}
Upon checking, $
x=45
$ satisfies the original equation.