Answer
$x=\left\{ \dfrac{3-i\sqrt{3}}{5},\dfrac{3+i\sqrt{3}}{5} \right\}
$
Work Step by Step
Taking the square root of both sides, the solutions to the given equation, $
(5x-3)^2=-3
,$ are
\begin{array}{l}\require{cancel}
5x-3=\pm\sqrt{-3}
\\\\
5x-3=\pm\sqrt{-1}\cdot\sqrt{3}
\\\\
5x-3=\pm i\sqrt{3}
\\\\
5x=3\pm i\sqrt{3}
\\\\
x=\dfrac{3\pm i\sqrt{3}}{5}
.\end{array}
Hence, the solutions are $
x=\left\{ \dfrac{3-i\sqrt{3}}{5},\dfrac{3+i\sqrt{3}}{5} \right\}
.$
