Answer
$x=6$
Work Step by Step
Given: $\sqrt {2x-3}=x-3$
Take square on both sides.
we have, $(\sqrt {2x-3})^2=(x-3)^2$
or, $2x-3=x^2-6x+9$
or, $x^2-8x+12=0$
Factoization as follows:
$(x-6)(x-2)=0$
or, $x=6,2$
Plug $x=6$ in the expression $\sqrt {2x-3}=x-3 \implies \sqrt {2(6)-3}=6-3 \implies 3 =3 $, we get the value of $x=6$ satisfies the expression.
