Solve nx=sqrt{a-3}

$$n x = \sqrt { a - 3 }$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=\frac{\sqrt{a-3}}{x}\text{, }&x\neq 0\\n\in \mathrm{C}\text{, }&a=3\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xn=\sqrt{a-3}$$

Divide both sides by x.

$$\frac{xn}{x}=\frac{\sqrt{a-3}}{x}$$

Dividing by x undoes the multiplication by x.

$$n=\frac{\sqrt{a-3}}{x}$$

Solve for a

$$a=\left(nx\right)^{2}+3$$

$$\left(n\leq 0\text{ and }x\leq 0\right)\text{ or }\left(x\geq 0\text{ and }n\geq 0\right)$$

Steps for Solving Radical Equations

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

$$\sqrt{a-3}=nx$$

Square both sides of the equation.

$$a-3=n^{2}x^{2}$$

Add 3 to both sides of the equation.

$$a-3-\left(-3\right)=n^{2}x^{2}-\left(-3\right)$$

Subtracting -3 from itself leaves 0.

$$a=n^{2}x^{2}-\left(-3\right)$$

Subtract -3 from n^{2}x^{2}.

$$a=n^{2}x^{2}+3$$

Solve for n

$$\left\{\begin{matrix}n=\frac{\sqrt{a-3}}{x}\text{, }&x\neq 0\text{ and }a\geq 3\\n\in \mathrm{R}\text{, }&x=0\text{ and }a=3\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xn=\sqrt{a-3}$$

Divide both sides by x.

$$\frac{xn}{x}=\frac{\sqrt{a-3}}{x}$$

Dividing by x undoes the multiplication by x.

$$n=\frac{\sqrt{a-3}}{x}$$

Solve for a (complex solution)

$$a=\left(nx\right)^{2}+3$$

$$arg(nx)<\pi \text{ or }x=0\text{ or }n=0$$