Answer
The solution of the equation $7{{x}^{2}}+2x+15=0$ is $x=-0.143\pm 1.46i$.
Work Step by Step
Use the quadratic formula $x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$,
$\begin{align}
& x=\frac{-2\pm \sqrt{{{2}^{2}}-4\left( 7 \right)\left( 15 \right)}}{2\left( 7 \right)} \\
& =\frac{-2\pm \sqrt{4-420}}{14} \\
& =\frac{-2\pm \sqrt{-416}}{14}
\end{align}$
$\sqrt{-1}=i$ and here $i$ is the imaginary number,
$\begin{align}
& x=\frac{-2\pm \sqrt{-416}}{14} \\
& =\frac{-2\pm \sqrt{416}i}{14} \\
& =\frac{-2}{14}\pm \frac{\sqrt{416}i}{14} \\
& =-0.143\pm 1.46i
\end{align}$
