\[\boxed{\text{686\ (686).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[3x^{2} + 2x + k = 0,\]
\[\ \ 2x_{1} = - 3x_{2} \Longrightarrow x_{1} = - 1,5x_{2}\]
\[x^{2} + \frac{2}{3}x + \frac{k}{3} = 0\]
\[Ответ:k = - 8\text{.\ }\]