\[ \begin{align} -&x^{2}+2x+2=0\\[5pt] \Delta=b^{2}-4ac&=2^{2}-4.(-1).2=4+8=12\\[5pt] x=\frac{-b\pm\sqrt{\Delta \;}}{2a}&=\frac{-2\pm \sqrt{12\;}}{2.(-1)}=\frac{-2\pm\sqrt{4.3}}{-2}=\\ &=\frac{-2\pm2\sqrt{3}}{-2}=\frac{-2.(1\pm \sqrt{3})}{-2}=\\ &=1\pm \sqrt{3}\hfill\\[5pt] x=1-&\sqrt{3}\qquad \text{ou}\qquad x=1+\sqrt{3} \end{align} \]