[tex]\begin{gathered} -x^2-2x+6=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ In\text{ this case} \\ a=-1 \\ b=-2 \\ c=6 \\ x=\frac{-(-2)\pm\sqrt[]{(-2)^2-4(-1)(6)}}{2(-1)} \\ \\ x=\frac{2\pm\sqrt[]{28}}{-2} \\ \\ x=\frac{2\pm2\sqrt[]{7}}{-2} \\ \\ x1=\frac{2+2\sqrt[]{7}}{-2} \\ \\ x1=-1-\sqrt[]{7} \\ x2=\frac{2-2\sqrt[]{7}}{-2} \\ x2=-1+\sqrt[]{7} \\ \\ \text{The solutions for the equation are }x1=-1-\sqrt[]{7}\text{ and} \\ \text{ }x2=-1+\sqrt[]{7} \end{gathered}[/tex]
