Solve x=y/x^2sqrt{xdivpi/θ2x}

$$x = \frac{ y }{ { x }^{ 2 } } \sqrt{ x \div \frac{ \pi }{ \theta 2x } }$$

Solve for y

$$y=\frac{\sqrt{\frac{\pi }{\theta _{2}}}x^{3}}{|x|}$$

$$x\neq 0\text{ and }\theta _{2}>0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}.

$$xx^{2}=y\sqrt{\frac{x}{\frac{\pi }{\theta _{2}x}}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$x^{3}=y\sqrt{\frac{x}{\frac{\pi }{\theta _{2}x}}}$$

Divide x by \frac{\pi }{\theta _{2}x} by multiplying x by the reciprocal of \frac{\pi }{\theta _{2}x}.

$$x^{3}=y\sqrt{\frac{x\theta _{2}x}{\pi }}$$

Multiply x and x to get x^{2}.

$$x^{3}=y\sqrt{\frac{x^{2}\theta _{2}}{\pi }}$$

Swap sides so that all variable terms are on the left hand side.

$$y\sqrt{\frac{x^{2}\theta _{2}}{\pi }}=x^{3}$$

The equation is in standard form.

$$\sqrt{\frac{\theta _{2}x^{2}}{\pi }}y=x^{3}$$

Divide both sides by \sqrt{x^{2}\theta _{2}\pi ^{-1}}.

$$\frac{\sqrt{\frac{\theta _{2}x^{2}}{\pi }}y}{\sqrt{\frac{\theta _{2}x^{2}}{\pi }}}=\frac{x^{3}}{\sqrt{\frac{\theta _{2}x^{2}}{\pi }}}$$

Dividing by \sqrt{x^{2}\theta _{2}\pi ^{-1}} undoes the multiplication by \sqrt{x^{2}\theta _{2}\pi ^{-1}}.

$$y=\frac{x^{3}}{\sqrt{\frac{\theta _{2}x^{2}}{\pi }}}$$

Divide x^{3} by \sqrt{x^{2}\theta _{2}\pi ^{-1}}.

$$y=\frac{\sqrt{\pi }x^{3}}{\sqrt{\theta _{2}}|x|}$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt[4]{\frac{\theta _{2}}{\pi }}\sqrt{y}\text{, }&y>0\text{ and }\theta _{2}>0\\x=-\sqrt[4]{\frac{\theta _{2}}{\pi }}\sqrt{-y}\text{, }&\theta _{2}>0\text{ and }y<0\end{matrix}\right.$$