$2x^4-x^3-11x^2-x+2=0$

The given equation is 

$\begin{array}{l}2x^4-x^3-11x^2-x+2=0\\ 2\left(x^2+\frac{1}{x^2}\right)-\left(x+\frac{1}{x}\right)-11=0\end{array}$

Put $x+\frac{1}{x}=t$

Then the given equation reduces to

$\begin{array}{l}2\left(t^2-2\right)-t-11=0\\ 2t^2-t-15=0\\ (t-3)(2t+5)=0\\ t=3,-\frac{5}{2}\\ x+\frac{1}{x}=3,-\frac{5}{2}\\ x^2-3x+1=0,2x^2+5x+2=0\\ x=\frac{3\sqrt{5}}{2},x=-2,-\frac{1}{2}\end{array}$

Hence, the solution set is

$\left\{-2,-\frac{1}{2},\frac{3\sqrt{5}}{2}\right\}$