Answer
$x=2$
Work Step by Step
Squaring both sides of the given equation, $
\sqrt{2x-3}=3-x
,$ then the solution/s is/are
\begin{array}{l}\require{cancel}
2x-3=(3)^2+2(3)(-x)+(-x)^2
\\\\
2x-3=9-6x+x^2
\\\\
-x^2+(2x+6x)+(-3-9)=0
\\\\
-x^2+8x-12=0
\\\\
x^2-8x+12=0
\\\\
(x-6)(x-2)=0
\\\\
x=\{ 2,6 \}
.\end{array}
Upon checking, only $
x=2
$ satisfies the original equation.