Solve fx=x^2-2bx+3b^2

$$fx = { x }^{ 2 } -2bx+3 { b }^{ 2 }$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=\frac{3b^{2}}{x}+x-2b\text{, }&x\neq 0\\f\in \mathrm{C}\text{, }&x=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xf=x^{2}-2bx+3b^{2}$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{x^{2}-2bx+3b^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{x^{2}-2bx+3b^{2}}{x}$$

Divide x^{2}-2bx+3b^{2} by x.

$$f=\frac{3b^{2}}{x}+x-2b$$

Solve for f

$$\left\{\begin{matrix}f=\frac{3b^{2}}{x}+x-2b\text{, }&x\neq 0\\f\in \mathrm{R}\text{, }&x=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xf=x^{2}-2bx+3b^{2}$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{x^{2}-2bx+3b^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{x^{2}-2bx+3b^{2}}{x}$$

Divide x^{2}-2bx+3b^{2} by x.

$$f=\frac{3b^{2}}{x}+x-2b$$

Solve for b (complex solution)

$$b=\frac{\sqrt{x\left(3f-2x\right)}+x}{3}$$

$$b=\frac{-\sqrt{x\left(3f-2x\right)}+x}{3}$$

Solve for b

$$b=\frac{\sqrt{x\left(3f-2x\right)}+x}{3}$$

$$b=\frac{-\sqrt{x\left(3f-2x\right)}+x}{3}\text{, }\left(x\leq 0\text{ or }f\geq \frac{2x}{3}\right)\text{ and }\left(x\geq 0\text{ or }f\leq \frac{2x}{3}\right)$$