Answer
$x=6$
Work Step by Step
Squaring both sides of the inequality and using the properties of radicals, the solution to the given equation, $
\sqrt{5x+6}=6
,$ is
\begin{array}{l}\require{cancel}\left(
\sqrt{5x+6}
\right)^2=\left(
6
\right)^2
\\\\
5x+6=36
\\\\
5x=36-6
\\\\
5x=30
\\\\
x=\dfrac{30}{5}
\\\\
x=6
.\end{array}
Upon checking, $
x=6
$ satisfies the original equation.
