[tex]-x^2+2x+7 =0\\\\a=-1,\ \ b=2,\ \ c=7\\\\\Delta =b^2-4ac=2^2-4*(-1)*7=4+28=32\\\\\sqrt{\Delta }=\sqrt{32}=\sqrt{16*2}=4\sqrt{2}\\\\x_{1} =\frac{-b-\sqrt{\Delta }}{2a}=\frac{-2-4\sqrt{2}}{2*(-1)}=\frac{-2(1+ 2\sqrt{2})}{-2}=1+2\sqrt{2}\\\\x_{2} =\frac{-b+ \sqrt{\Delta }}{2a}=\frac{-2+4\sqrt{2}}{2*(-1)}=\frac{-2(1-2\sqrt{2})}{-2}=1-2\sqrt{2}[/tex]
