[tex]\displaystyle\\
x^2 - 7x - 34 = 10\\\\
x^2 - 7x - 34 -10=0\\\\
x^2 - 7x - 44 =0\\\\
x_{12}= \frac{-b \pm \sqrt{b^2-4ac} }{2a}= \frac{7 \pm \sqrt{7^2-4\cdot1\cdot (-44)} }{2\cdot 1}= \\\\
=\frac{7\pm \sqrt{49+176}}{2}=\frac{7\pm \sqrt{225}}{2}=\frac{7\pm 15}{2}\\\\
x_1 = \frac{7 + 15}{2}=\frac{22}{2} = \boxed{11}\\\\
x_2 =\frac{7 - 15}{2}=\frac{-8}{2} = \boxed{-4} [/tex]
