Решите неравенство: 1/2 x^2-3/2 x-5<0.

\[\frac{1}{2}x^{2} - \frac{3}{2}x - 5 < 0\ \ \ \ | \cdot 2\]

\[x^{2} - 3x - 10 < 0\]

\[D = ( - 3)^{2} - 4 \cdot 1 \cdot ( - 10) =\]

\[= 9 + 40 = 49\]

\[x_{1} = \frac{3 + \sqrt{49}}{2 \cdot 1} = \frac{3 + 7}{2} = \frac{10}{2} = 5;\ \ \ \ \ \]

\[x_{2} = \frac{3 - \sqrt{49}}{2 \cdot 1} = \frac{3 - 7}{2} =\]

\[= - \frac{4}{2} = - 2\]

\[Ответ:( - 2;5).\]