\[\boxed{\text{678\ (678).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[4x^{2} + bx - 27 = 0,\]
\[\text{\ \ }x_{1}\ :x_{2} = - 3\mathbf{\Longrightarrow}x_{1} = - 3 \cdot x_{2}\]
\[x^{2} + \frac{b}{4}x - \frac{27}{4} = 0\]
\[\left\{ \begin{matrix} b = 8x_{2} \\ x_{2}^{2} = \frac{9}{4} \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} b = 8x_{2} \\ x_{2} = \pm \frac{3}{2} \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]
\[Ответ:b = \pm 12.\ \]