Answer
$x=\dfrac{11}{5}$
Work Step by Step
Squaring both sides of the given equation, $
\sqrt{5x-2}=3
,$ then,
\begin{array}{l}\require{cancel}
\left( \sqrt{5x-2} \right)^2=(3)^2
\\\\
5x-2=9
\\\\
5x=9+2
\\\\
5x=11
\\\\
x=\dfrac{11}{5}
.\end{array}
Upon checking, $
x=\dfrac{11}{5}
$ satisfies the original equation.
