Solve for f_8
f_{8}=\frac{x-2}{x^{2}}
x\neq 0
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{\sqrt{1-8f_{8}}+1}{2f_{8}}\text{; }x=\frac{-\sqrt{1-8f_{8}}+1}{2f_{8}}\text{, }&f_{8}\neq 0\\x=2\text{, }&f_{8}=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{\sqrt{1-8f_{8}}+1}{2f_{8}}\text{; }x=\frac{-\sqrt{1-8f_{8}}+1}{2f_{8}}\text{, }&f_{8}\neq 0\text{ and }f_{8}\leq \frac{1}{8}\\x=2\text{, }&f_{8}=0\end{matrix}\right.
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f_{8}x^{2}+2=x
Add x to both sides. Anything plus zero gives itself.
f_{8}x^{2}=x-2
Subtract 2 from both sides.
x^{2}f_{8}=x-2
The equation is in standard form.
\frac{x^{2}f_{8}}{x^{2}}=\frac{x-2}{x^{2}}
Divide both sides by x^{2}.
f_{8}=\frac{x-2}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
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