\[x^{2} - 3x + m = 0\]
\[3x_{1} - 4x_{2} = 37\]
\[\left\{ \begin{matrix} x_{1} + x_{2} = 3 \\ x_{1} \cdot x_{2} = m \\ \end{matrix} \right.\ \]
\[1)\ x_{1} = 3 - x_{2}\ \]
\[3 \cdot \left( 3 - x_{2} \right) - 4x_{2} = 37\]
\[9 - 3x_{2} - 4x_{2} = 37\ \ \]
\[- 7x_{2} = 28\]
\[x_{2} = - 4.\]
\[2)\ x_{1} = 3 - ( - 4) = 3 + 4 = 7.\]
\[3)\ 7 \cdot ( - 4) = m \Longrightarrow m = - 28.\]
\[Ответ:\ \ x_{1} = 7;\ \ x_{2} = - 4;\ \ \]
\[m = - 28.\]