\[x² + x\left( 1 - \sqrt{5} \right) - \sqrt{5} = 0\]
\[D = \left( 1 - \sqrt{5} \right)^{2} - 4 \cdot 1 \cdot \left( - \sqrt{5} \right) =\]
\[= 1 - 2\sqrt{5} + 5 + 4\sqrt{5} = 6 + 2\sqrt{5}\]
\[\sqrt{6 + 2\sqrt{5}\ } = \sqrt{1 + 2\sqrt{5} + 5} =\]
\[= \sqrt{\left( 1 + \sqrt{5} \right)^{2}} = 1 + \sqrt{5}\]
\[x_{1} = \frac{- \left( 1 - \sqrt{5} \right) - \left( 1 + \sqrt{5} \right)}{2 \cdot 1} =\]
\[= \frac{- 1 + \sqrt{5} - 1 - \sqrt{5}}{2} =\]
\[= - \frac{- 2}{2} = - 1;\]
\[x_{2} = \frac{- \left( 1 - \sqrt{5} \right) + 1 + \sqrt{5}}{2 \cdot 1} =\]
\[= \frac{- 1 + \sqrt{5} + 1 + \sqrt{5}}{2} =\]
\[= \frac{2\sqrt{5}}{2} = \sqrt{5}.\]
\[Ответ:\ x = - 1;\ x = \sqrt{5}.\]