$\begin{array} { l }\frac{ 4 }{ x }=\frac{ x }{ 9 },& x≠0\end{array}$
Simplify the equation using cross-multiplication$36={x}^{2}$
Swap the sides of the equation${x}^{2}=36$
Take the square root of both sides of the equation and remember to use both positive and negative roots$x=6$
Write the solutions, one with a $+$ sign and one with a $-$ sign$\begin{array} { l }\begin{array} { l }x=-6,\\x=6\end{array},& x≠0\end{array}$
Check if the solution is in the defined range$\begin{array} { l }x=-6,\\x=6\end{array}$
The equation has $2$ solutions$\begin{array} { l }x_1=-6,& x_2=6\end{array}$