Answer
$-2-\sqrt{5}\ i$; $-2+\sqrt{5}\ i$
Work Step by Step
Given \begin{equation}
-b^2-4 b+6=15.
\end{equation} This equation can be best solved by using the quadratic formula.
\begin{equation}
\begin{aligned}
-b^2-4 b+6&=15\\
-b^2-4 b-9&=0\\
b^2+4 b+9&=0\\
b&=\frac{-4 \pm \sqrt{4^2-4 \cdot 1 \cdot 9}}{2 \cdot 1}\\
b&= \frac{-4 \pm \sqrt{-20} }{2 }\\
&=\frac{-4 \pm 2 \sqrt{5}i}{2 }\\
& = -2\pm \sqrt 5\ i.
\end{aligned}
\end{equation} The solution is \begin{equation}
b=-2-\sqrt{5}\ i\ ,\quad b=-2+\sqrt{5}\ i.
\end{equation}
