Решите уравнение: корень из (x-4)=19-4x.

\[\sqrt{x - 4} = 19 - 4x;\ \ \ \ \ \ t = \sqrt{x - 4}\]

\[4t^{2} + t - 3 = 0\]

\[t_{1} = - 1;\ \ \ t_{2} = \frac{3}{4}\]

\[1)\ \sqrt{x - 4} = - 1;\ \ \ \]

\[\sqrt{x - 4} \geq 0 \Longrightarrow нет\ решения.\]

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

\[x - 4 = \frac{9}{16}\]

\[x = 4\frac{9}{16}\]

\[Ответ:\ 4\frac{9}{16}.\]