$$(3k+1)x^{2}+2(k+1)ox+k=0$$
$k=-\frac{x\left(x+2o\right)}{3x^{2}+2ox+1}$
$\left(x\neq \frac{\sqrt{o^{2}-3}-o}{3}\text{ and }x\neq \frac{-\sqrt{o^{2}-3}-o}{3}\right)\text{ or }|o|<\sqrt{3}$
$\left\{\begin{matrix}o=-\frac{3kx^{2}+x^{2}+k}{2x\left(k+1\right)}\text{, }&k\neq -1\text{ and }x\neq 0\\o\in \mathrm{R}\text{, }&k=0\text{ and }x=0\end{matrix}\right.$
