Answer
$x=\dfrac{4}{7}$
Work Step by Step
Raising both sides of the given equation, $
\sqrt[]{7x-4}=\sqrt[]{4-7x}
,$ to the second power, then the solution/s is/are
\begin{array}{l}\require{cancel}
7x-4=4-7x
\\\\
7x+7x=4+4
\\\\
14x=8
\\\\
x=\dfrac{8}{14}
\\\\
x=\dfrac{\cancel{2}\cdot4}{\cancel{2}\cdot7}
\\\\
x=\dfrac{4}{7}
.\end{array}
Upon checking, $
x=\dfrac{4}{7}
$ satisfies the original equation.