\[x^{2} - 25x + c = 0\]
\[x_{1}\ :x_{2} = 2\ :3\ \ \]
\[x_{1} = \frac{2}{3} \cdot x_{2}\]
\[\left\{ \begin{matrix} x_{1} + x_{2} = 25 \\ x_{1} \cdot x_{2} = c\ \ \ \\ \end{matrix} \right.\ \]
\[1)\ \frac{2}{3}x_{2} + x_{2} = 25\]
\[\frac{5}{3}x_{2} = 25\]
\[x_{2} = 25 \cdot \frac{3}{5} = 15.\]
\[2)\ x_{1} = \frac{2}{3} \cdot 15 = 10.\ \ \]
\[3)\ 10 \cdot 15 = c \Longrightarrow c = 150.\]
\[Ответ:\ x_{1} = 10;\ \ x_{2} = 15;\ \ \]
\[c = 150.\]