\[x^{2} + 2x + q = 0;\ \ \ \ \ \]
\[\frac{x_{1}}{x_{2}} = 6 \Longrightarrow x_{1} = 6x_{2}\]
\[{q = x}_{1} \cdot x_{2} =\]
\[= \left( - \frac{12}{7} \right) \cdot \left( - \frac{2}{7} \right) = \frac{24}{49}\]
\[Ответ:x_{1} = - \frac{12}{7};\ \ x_{2} = - \frac{2}{7};\ \ \]
\[q = \frac{24}{49}.\]