Решите неравенство: x^2+8x+7>0.

\[x^{2} + 8x + 7 > 0\]

\[D = 8^{2} - 4 \cdot 1 \cdot 7 =\]

\[= 64 - 28 = 36\]

\[x_{1} = \frac{- 8 + \sqrt{36}}{2 \cdot 1} = \frac{- 8 + 6}{2} =\]

\[= - \frac{2}{2} = - 1;\ \ \ \ \ \]

\[x_{2} = \frac{- 8 - \sqrt{36}}{2 \cdot 1} = \frac{- 8 - 6}{2} =\]

\[= - \frac{14}{2} = - 7\]

\[Ответ:( - \infty; - 7) \cup ( - 1; + \infty).\]