Answer
$x=6$
Work Step by Step
By squaring both sides of the equal sign, the values of $x$ that satisfy the equation $
\sqrt{2x-3}=x-3
$ are
\begin{array}{l}
\left( \sqrt{2x-3} \right)^2=(x-3)^2
\\\\
2x-3=x^2-6x+9
\\\\
x^2-8x+12=0
\\\\
(x-6)(x-2)=0
\\\\
x=\{2,6\}
.\end{array}
Upon checking, only $
x=6
$ satisfies the given equation.
