Solve for k
k=-\frac{4-9x}{x^{2}}
x\neq 0
Solve for x (complex solution)
\left\{\begin{matrix}x=-\frac{\sqrt{81-16k}-9}{2k}\text{; }x=\frac{\sqrt{81-16k}+9}{2k}\text{, }&k\neq 0\\x=\frac{4}{9}\text{, }&k=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=-\frac{\sqrt{81-16k}-9}{2k}\text{; }x=\frac{\sqrt{81-16k}+9}{2k}\text{, }&k\neq 0\text{ and }k\leq \frac{81}{16}\\x=\frac{4}{9}\text{, }&k=0\end{matrix}\right.
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kx^{2}-8x+4=x
Swap sides so that all variable terms are on the left hand side.
kx^{2}+4=x+8x
Add 8x to both sides.
kx^{2}+4=9x
Combine x and 8x to get 9x.
kx^{2}=9x-4
Subtract 4 from both sides.
x^{2}k=9x-4
The equation is in standard form.
\frac{x^{2}k}{x^{2}}=\frac{9x-4}{x^{2}}
Divide both sides by x^{2}.
k=\frac{9x-4}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
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