Решите уравнение: 3x-2корень из x-8=0.

\[3x - 2\sqrt{x} - 8 = 0\]

\[Пусть\ \ t = \sqrt{x}:\]

\[3t^{2} - 2t - 8 = 0\]

\[D = 4 + 96 = 100\]

\[t_{1,2} = \frac{2 \pm 10}{6} = 2;\ - \frac{4}{3}\]

\[\sqrt{x} = 2\ \ \ \ \ \ \ \ \ \ \ \sqrt{x} = - \frac{4}{3}\]

\[x = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \varnothing\]

\[Ответ:\ 4.\]