$$x^{4}-x^{2}-2x-1=0$$
$x=\frac{-1+\sqrt{3}i}{2}\approx -0.5+0.866025404i$
$x=\frac{-\sqrt{3}i-1}{2}\approx -0.5-0.866025404i$
$x=\frac{1-\sqrt{5}}{2}\approx -0.618033989$
$x = \frac{\sqrt{5} + 1}{2} \approx 1.618033989$
$x = \frac{\sqrt{5} + 1}{2} \approx 1.618033989$
$x=\frac{1-\sqrt{5}}{2}\approx -0.618033989$