[tex]\displaystyle\\
8x^2 +2x +1 =0\\\\
x_{12}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-2\pm \sqrt{2^2-4\cdot 8 \cdot 1}}{2\cdot 8}=\\\\
=\frac{-2\pm \sqrt{4-32}}{16}=\frac{-2\pm \sqrt{-28}}{16}=\frac{-2\pm \sqrt{4\cdot 7\cdot(-1)}}{16}=\\\\
=\frac{-2\pm 2i\sqrt{7}}{16}=\frac{-1\pm i\sqrt{7}}{8}= -\frac{1}{8}\pm \frac{\sqrt{7}}{8}i\\\\
x_1 = \boxed{-\frac{1}{8}+ \frac{\sqrt{7}}{8}i}\\\\
x_2 = \boxed{-\frac{1}{8}- \frac{\sqrt{7}}{8}i}\\\\
x_1,~x_2~\in \mathbb{C}[/tex]
