[tex]\bf ~~~~~~~~~~~~\textit{quadratic formula}
\\\\
\begin{array}{lcccl}
y=& 7 x^2& +2 x& +8\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}
\qquad \qquad
x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}
\\\\\\
x=\cfrac{-2\pm\sqrt{2^2~-~4(7)(8)}}{2(7)}\implies x=\cfrac{-2\pm\sqrt{4-224}}{14}
\\\\\\
x=\cfrac{-2\pm\sqrt{-220}}{14}\implies x=\cfrac{-2\pm\sqrt{2^2\cdot -55}}{14}[/tex]
[tex]\bf x=\cfrac{-2\pm 2\sqrt{-55}}{14}\implies x=\cfrac{-1\pm 1\sqrt{-55}}{7}
\\\\\\
x=\cfrac{-1\pm \sqrt{55\cdot -1}}{7}\implies x=\cfrac{-1\pm \sqrt{55}\cdot \sqrt{-1}}{7}
\\\\\\
x=\cfrac{-1\pm \sqrt{55}~i}{7}\implies x=
\begin{cases}
-\frac{1}{7}+\frac{i\sqrt{55}}{7}\\\\
-\frac{1}{7}-\frac{i\sqrt{55}}{7}
\end{cases}[/tex]
