\[(b + 5)x² + (2b + 10)x + 4 = 0\ \ \]
\[b + 5 = 0 \Longrightarrow b = - 5\]
\[= 4b^{2} + 24b + 20 =\]
\[= 4 \cdot \left( b^{2} + 2b + 5 \right)\]
\[4 \cdot \left( b^{2} + 6b + 5 \right) = 0\]
\[b^{2} + 6b + 5 = 0\]
\[D = 6^{2} - 4 \cdot 1 \cdot 5 =\]
\[= 36 - 20 = 16\]
\[b_{1} = \frac{- 6 + \sqrt{16}}{2} = \frac{- 6 + 4}{2} =\]
\[= - \frac{2}{2} = - 1\]
\[b_{2} = \frac{- 6 - \sqrt{16}}{2} = \frac{- 6 - 4}{2} =\]
\[= - \frac{10}{2} = - 5\]
\[Ответ:\ при\ \ b = - 1;\ b = - 5.\]