real analysis - Does $x_n$ converge where $x_{n+1}=-16+ 6x_n+frac{12}{x_n}$

Define $x_{n+1}=-16+ 6x_n+\frac{12}{x_n} \hspace{0.2cm} \forall n\in \mathbb{N}$ where $x_1\neq 2$. I need to find whether it diverges or converges?

I tried proving $\{x_n\}$ is increasing/ decreasing and bounded, but nothing really worked. I guess that it should diverge!