Answer
$-1-i\frac{\sqrt{391}}{23}$; $-1+ i\frac{\sqrt{391}}{23} $
Work Step by Step
Given \begin{equation}
2.3 x^2+4.6 x+9=5.
\end{equation} Use the quadratic formula to solve for $x$.
\begin{equation}
\begin{aligned}
2.3 x^2+4.6 x+9&=5\\
(2.3 x^2+4.6 x+4)\cdot 10&= 0\cdot 10\\
23 x^2+46 x+40& = 0\\
x&=\frac{-46 \pm \sqrt{46^2-4 \cdot 23 \cdot 40}}{2 \cdot 23}\\
x&=\frac{-46 \pm \sqrt{-1564}}{2 \cdot 23}\\
x& = \frac{-46 \pm i \sqrt{4\cdot 391}}{2 \cdot 23}\\
x& = \frac{-46 \pm 2i\sqrt{391}}{2 \cdot 23}\\
x& = \frac{-23 \pm i \sqrt{391}}{ 23}.
\end{aligned}
\end{equation} The solution is $$ x= -1- i\frac{\sqrt{391}}{23}, \quad x= -1+ i\frac{\sqrt{391}}{23}. $$
