Answer
$x=2$
Work Step by Step
Simplify. $ \sqrt{2x-3}=3-x$
Take square on both sides.
we have, $ (\sqrt{2x-3})^2=(3-x)^2$
or, $2x-3=9+x^2-6x+3$
or, $ x^2-6x-2x+12=0$
Thus, $x^2-8x+12=0$
Now, apply factoziation.
$(x-6)(x-2)=0$
or, $x=2,6$
Plug $x=2$ in the equation $ \sqrt{2x-3}=3-x \implies \sqrt{2(2)-3}=3-2 \implies 1=1$
Hence, we can conclude that $x=2$ satisfies the expression.
