# Solve for: (4)/(x)=(x)/(9)

## Expression: $\frac{ 4 }{ x }=\frac{ x }{ 9 }$

Determine the defined range

$\begin{array} { l }\frac{ 4 }{ x }=\frac{ x }{ 9 },& x≠0\end{array}$

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

$\begin{array} { l }x_1=-6,& x_2=6\end{array}$

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