Решите неравенство: 12x/(x+4)-5*корень из (12x/(x+4))-6>=0.

\[\frac{12x}{x + 4} - 5\sqrt{\frac{12x}{x + 4}} - 6 \geq 0\]

\[t = \sqrt{\frac{12x}{x + 4}}\]

\[t^{2} - 5t - 6 \geq 0\]

\[(t - 6)(t + 1) \geq 0\]

\[t \leq - 1;\ \ \ \ t \geq 6\]

\[1)\ \sqrt{\frac{12x}{x + 4}} \leq - 1;\ \ \ \ \]

\[\sqrt{\frac{12x}{x + 4}} \geq 0 \Longrightarrow нет\ решения.\]

\[2)\ \sqrt{\frac{12x}{x + 4}} \geq 6\]

\[\frac{12x}{x + 4} \geq 36\]

\[\frac{12x - 36 \cdot (x + 4)}{x + 4} \geq 0\]

\[\frac{12x - 36x - 144}{x + 4} \geq 0\]

\[\frac{- 24x - 144}{x + 4} \geq 0\]

\[\frac{- 24 \cdot (x + 6)}{x + 4} \geq 0\]

\[\frac{x + 6}{x + 4} \leq 0\]

\[Ответ:\lbrack - 6;\ - 4).\]