Решите уравнение корень из (9x^2-24x+16)=5.

\[\left( \sqrt{9x^{2} - 24x + 16} \right)^{2} = (5)^{2}\]

\[9x^{2} - 24x + 16 = 25\]

\[9x² - 24x - 9 = 0\ \ \ \ |\ :3\]

\[3x² - 8x - 3 = 0\]

\[D = 64 + 36 = 100\]

\[x_{1,2} = \frac{8 \pm 10}{6} = 3;\ - \frac{1}{3}.\]

\[Ответ:\ \ 3;\ - \frac{1}{3}.\]