#### Answer

$x=\dfrac{2b\pm\sqrt{3a}}{5}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To find the solutions of the given equation, $
(5x-2b)^2=3a
,$ take the square root of both sides ((Square Root Property). Then use the properties of equality to isolate $x.$
$\bf{\text{Solution Details:}}$
Taking the square root of both sides and then simplifying the radical, the equation above is equivalent to
\begin{array}{l}\require{cancel}
5x-2b=\pm\sqrt{3a}
.\end{array}
Using the properties of equality to isolate $x$, the given equation is equivalent to
\begin{array}{l}\require{cancel}
5x=2b\pm\sqrt{3a}
\\\\
x=\dfrac{2b\pm\sqrt{3a}}{5}
.\end{array}