Решите неравенство: |x^2-x-8|<12.

\[\left| x^{2} - x - 8 \right| < 12\]

\[\left\{ \begin{matrix} x^{2} - x - 8 > - 12 \\ x^{2} - x - 8 < 12\ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x² - x + 4 > 0\ \ \\ x² - x - 20 < 0 \\ \end{matrix} \right.\ \]

\[x^{2} - x + 4 > 0\]

\[D = 1 - 16 < 0 - x \in R.\]

\[x^{2} - x - 20 < 0\]

\[x_{1} + x_{2} = 1;\ \ x_{1} \cdot x_{2} = - 20\]

\[x_{1} = 5;\ \ x_{2} = - 4\]

\[(x + 4)(x - 5) < 0\]

\[- 4 < x < 5.\]

\[Ответ:( - 4;5).\]