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[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]

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