Answer
$x=\pm\dfrac{8\sqrt{7}}{7}$
Work Step by Step
Multiplying both sides by the $LCD=
8x^2
,$ the solution/s to the given equation, $
\dfrac{7}{8}=\dfrac{8}{x^2}
,$ is/are
\begin{array}{l}\require{cancel}
x^2(7)=8(8)
\\\\
7x^2=64
\\\\
x^2=\dfrac{64}{7}
\\\\
x=\pm\sqrt{\dfrac{64}{7}}
\\\\
x=\pm\dfrac{\sqrt{64}}{\sqrt{7}}
\\\\
x=\pm\dfrac{8}{\sqrt{7}}
\\\\
x=\pm\dfrac{8}{\sqrt{7}}\cdot\dfrac{\sqrt{7}}{\sqrt{7}}
\\\\
x=\pm\dfrac{8\sqrt{7}}{(\sqrt{7})^2}
\\\\
x=\pm\dfrac{8\sqrt{7}}{7}
.\end{array}
