How to solve $2x^5+5\sqrt{2}x^4+20x^3+20\sqrt{2}x^2+20x+4\sqrt{2}=0$? 
How to solve $$2x^5+5\sqrt{2}x^4+20x^3+20\sqrt{2}x^2+20x+4\sqrt{2}=0?$$

I just have no idea and I'have some knowledge about the polynomial equations. Here, just nothing. 

The only real root is
$$
\alpha=-\frac{1}{\sqrt{2}}=- 0.707106781187\cdots 
$$
The polynomial divided by $x-\alpha$ then has degree $4$ and has roots $\alpha\pm i\beta$, $\alpha\pm i \gamma$.
