Solve for f (complex solution)
\left\{\begin{matrix}f=\frac{x^{2}-2bx+3b^{2}}{rx}\text{, }&x\neq 0\text{ and }r\neq 0\\f\in \mathrm{C}\text{, }&\left(x=0\text{ and }b=0\right)\text{ or }\left(x=b-\sqrt{-2b^{2}}\text{ and }r=0\text{ and }b\neq 0\right)\text{ or }\left(x=\sqrt{-2b^{2}}+b\text{ and }r=0\text{ and }b\neq 0\right)\end{matrix}\right.
Solve for f
\left\{\begin{matrix}f=\frac{x^{2}-2bx+3b^{2}}{rx}\text{, }&r\neq 0\text{ and }x\neq 0\\f\in \mathrm{R}\text{, }&x=0\text{ and }b=0\end{matrix}\right.
Solve for b (complex solution)
b=\frac{\sqrt{x\left(3fr-2x\right)}+x}{3}
b=\frac{-\sqrt{x\left(3fr-2x\right)}+x}{3}
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rxf=x^{2}-2bx+3b^{2}
The equation is in standard form.
\frac{rxf}{rx}=\frac{x^{2}-2bx+3b^{2}}{rx}
Divide both sides by rx.
f=\frac{x^{2}-2bx+3b^{2}}{rx}
Dividing by rx undoes the multiplication by rx.
rxf=x^{2}-2bx+3b^{2}
The equation is in standard form.
\frac{rxf}{rx}=\frac{x^{2}-2bx+3b^{2}}{rx}
Divide both sides by rx.
f=\frac{x^{2}-2bx+3b^{2}}{rx}
Dividing by rx undoes the multiplication by rx.
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