Answer
$x=9$
Work Step by Step
Squaring both sides of the given equation, $
\sqrt{x+4}=\sqrt{2x-5}
,$ then the solution/s is/are
\begin{array}{l}\require{cancel}
x+4=2x-5
\\\\
x-2x=-5-4
\\\\
-x=-9
\\\\
x=9
.\end{array}
Upon checking, $
x=9
$ satisfies the original equation.