Solve for k
k=\frac{5x+3}{x^{2}}
x\neq 0
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{\sqrt{12k+25}+5}{2k}\text{; }x=\frac{-\sqrt{12k+25}+5}{2k}\text{, }&k\neq 0\\x=-\frac{3}{5}\text{, }&k=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{\sqrt{12k+25}+5}{2k}\text{; }x=\frac{-\sqrt{12k+25}+5}{2k}\text{, }&k\neq 0\text{ and }k\geq -\frac{25}{12}\\x=-\frac{3}{5}\text{, }&k=0\end{matrix}\right.
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kx^{2}=3+5x
Add 5x to both sides.
x^{2}k=5x+3
The equation is in standard form.
\frac{x^{2}k}{x^{2}}=\frac{5x+3}{x^{2}}
Divide both sides by x^{2}.
k=\frac{5x+3}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
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