Solve the equation $x^4-5x^2+6=0$

You can factor the expression as follows
\[x^4-5x^2+6=(x^2-2)(x^2-3)=0.\]
Thus  $x^2-2=0$ or $x^2-3=0$. So
\[x^2=2  \Rightarrow x=\pm \sqrt{2}\]
\[x^2=3  \Rightarrow  x=\pm \sqrt{3}.\]
Thus there are four solutions $\pm \sqrt{2}$  and  $\pm \sqrt{3}$.