Найдите множество решений неравенства: (x^2+x)/2-(8x-1)/3<-2.

\[\frac{x^{2} + x}{2} - \frac{8x - 1}{3} < - 2\ \ \ | \cdot 6\]

\[3x^{2} + 3x - 16x + 2 + 12 < 0\]

\[3x^{2} - 13x + 14 < 0\]

\[D = 169 - 168 = 1\]

\[x_{1} = \frac{13 - 1}{6} = 2\]

\[x_{2} = \frac{13 + 1}{6} = \frac{7}{3}\]

\[Ответ:\left( 2;2\frac{1}{3} \right).\]