Answer
$x=\dfrac{4}{7}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\sqrt{7x-4}=\sqrt{4-7x}
,$ raise both sides to the exponent equal to the index of the radical. Then use the properties of equality to isolate the variable. Finally, do checking of the solution/s with the original equation.
$\bf{\text{Solution Details:}}$
Get rid of the radical symbol by raising both sides of the equation above to the exponent equal to $
2
$ (the same index as the radical). This results to
\begin{array}{l}\require{cancel}
(\sqrt{7x-4})^2=(\sqrt{4-7x})^2
\\\\
7x-4=4-7x
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
7x+7x=4+4
\\\\
14x=8
\\\\
x=\dfrac{8}{14}
\\\\
x=\dfrac{4}{7}
.\end{array}
Upon checking, $
x=\dfrac{4}{7}
$ satisfies the original equation.