Solve for k
k=-\frac{3-10x}{x^{2}}
x\neq 0
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{\sqrt{25-3k}+5}{k}\text{; }x=\frac{-\sqrt{25-3k}+5}{k}\text{, }&k\neq 0\\x=\frac{3}{10}\text{, }&k=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{\sqrt{25-3k}+5}{k}\text{; }x=\frac{-\sqrt{25-3k}+5}{k}\text{, }&k\neq 0\text{ and }k\leq \frac{25}{3}\\x=\frac{3}{10}\text{, }&k=0\end{matrix}\right.
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kx^{2}+3=10x
Add 10x to both sides. Anything plus zero gives itself.
kx^{2}=10x-3
Subtract 3 from both sides.
x^{2}k=10x-3
The equation is in standard form.
\frac{x^{2}k}{x^{2}}=\frac{10x-3}{x^{2}}
Divide both sides by x^{2}.
k=\frac{10x-3}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
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