Answer
$x=\left\{ 1,\dfrac{9}{4} \right\}$
Work Step by Step
The given quadratic equation, $
(2x-3)^2=x
,$ is equivalent to
\begin{array}{l}\require{cancel}
(2x)^2+2(2x)(-3)+(-3)^2=x
\\\\
4x^2-12x+9=x
\\\\
4x^2+(-12x-x)+9=0
\\\\
4x^2-13x+9=0
.\end{array}
Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, the solutions of the above quadratic equation are
\begin{array}{l}\require{cancel}
x=\dfrac{-(-13)\pm\sqrt{(-13)^2-4(4)(9)}}{2(4)}
\\\\
x=\dfrac{13\pm\sqrt{169-144}}{8}
\\\\
x=\dfrac{13\pm\sqrt{25}}{8}
\\\\
x=\dfrac{13\pm5}{8}
\\\\
x=\left\{ 1,\dfrac{9}{4} \right\}
.\end{array}
