[tex]given \: equation: {x}^{2} + 8x + 20= 0 \\ \\ x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ x = \frac{ -8 \pm \sqrt{ {8}^{2} - 4 \times 1 \times 20} }{2 \times 1} \\ \\ x = \frac{-8 \pm \sqrt{64-80} }{2} \\ \\ x = \frac{-8 \pm \sqrt{-16} }{2} \\ \\ x = \frac{-8 \pm 4i }{2} \\ \\x = \frac{-8 + 4i }{2} \: \: and \: \: \frac{-8 - 4i }{2}\\ \\ \boxed{x = -4+2i \ \ and\ \ -4-2i}[/tex]
