Answer
$x=\frac{3-\sqrt 5}{8},\frac{3+\sqrt 5}{8}$
Work Step by Step
$(8x-3)^{2}=5$
$8x-3=\sqrt 5$
$8x-3=-\sqrt 5$
$x=\frac{3-\sqrt 5}{8},\frac{3+\sqrt 5}{8}$
Take the square root of both sides. Then isolate $x$ from both of the resulting equations to get two answers.