Solve nmux=frac{sqrt{q}}{q}

$$n \mu x = \frac { \sqrt { q } } { q }$$

Solve for n (complex solution)

$$n=\frac{q^{-\frac{1}{2}}}{x\mu }$$

$$q\neq 0\text{ and }x\neq 0\text{ and }\mu \neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by q.

$$n\mu xq=\sqrt{q}$$

The equation is in standard form.

$$qx\mu n=\sqrt{q}$$

Divide both sides by \mu xq.

$$\frac{qx\mu n}{qx\mu }=\frac{\sqrt{q}}{qx\mu }$$

Dividing by \mu xq undoes the multiplication by \mu xq.

$$n=\frac{\sqrt{q}}{qx\mu }$$

Divide \sqrt{q} by \mu xq.

$$n=\frac{q^{-\frac{1}{2}}}{x\mu }$$

Solve for n

$$n=\frac{1}{\sqrt{q}x\mu }$$

$$x\neq 0\text{ and }\mu \neq 0\text{ and }q>0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by q.

$$n\mu xq=\sqrt{q}$$

The equation is in standard form.

$$qx\mu n=\sqrt{q}$$

Divide both sides by \mu xq.

$$\frac{qx\mu n}{qx\mu }=\frac{\sqrt{q}}{qx\mu }$$

Dividing by \mu xq undoes the multiplication by \mu xq.

$$n=\frac{\sqrt{q}}{qx\mu }$$

Divide \sqrt{q} by \mu xq.

$$n=\frac{1}{\sqrt{q}x\mu }$$

Solve for q (complex solution)

$$q=\frac{1}{\left(nx\mu \right)^{2}}$$

$$arg(\sqrt{\frac{1}{\left(nx\mu \right)^{2}}}nx\mu )<\pi \text{ and }x\neq 0\text{ and }\mu \neq 0\text{ and }n\neq 0$$

Solve for q

$$q=\frac{1}{\left(nx\mu \right)^{2}}$$

$$\left(x<0\text{ and }n<0\text{ and }\mu >0\right)\text{ or }\left(x<0\text{ and }n>0\text{ and }\mu <0\right)\text{ or }\left(x>0\text{ and }n>0\text{ and }\mu >0\right)\text{ or }\left(x>0\text{ and }n<0\text{ and }\mu <0\right)$$