[tex]\displaystyle\\
(5-x)(5+x)=(x-4)^2-7\\\\
5^2 - x^2 = x^2-8x + 16 -7\\\\
-x^2 -x^2+8x + 25 -16+7=0\\\\
-2x^2 + 8x +16=0\\\\
x_{12}= \frac{-b\pm \sqrt{b^2-4ac} }{2a}= \frac{-8\pm \sqrt{64-4\cdot(-2)\cdot 16} }{2\cdot(-2)}=\\\\
= \frac{-8\pm \sqrt{64+ 128} }{-4}= \frac{-8\pm \sqrt{192} }{-4}= \frac{-8\pm \sqrt{64\cdot 3} }{-4}=\\\\
=\frac{-8\pm 8\sqrt{ 3} }{-4}=2\mp 2\sqrt{ 3}\\\\
\boxed{\bf x_1 = 2-2\sqrt{ 3}}\\\\
\boxed{\bf x_2 = 2+2\sqrt{ 3}}[/tex]
