Answer
$x=\dfrac{21\pm\sqrt{41}}{50}$
Work Step by Step
The given quadratic equation, $
(5a-2)^2-a=0
,$ is equivalent to
\begin{array}{l}\require{cancel}
(5a)^2+2(5a)(-2)+(-2)^2-a=0
\\\\
25a^2-20a+4-a=0
\\\\
25a^2-21a+4=0
.\end{array}
Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, the solutions of the quadratic equation above are
\begin{array}{l}\require{cancel}
x=\dfrac{-(-21)\pm\sqrt{(-21)^2-4(25)(4)}}{2(25)}
\\\\
x=\dfrac{21\pm\sqrt{441-400}}{50}
\\\\
x=\dfrac{21\pm\sqrt{41}}{50}
.\end{array}
