[tex] {x}^{2} + 12x + 8 = 0[/tex]
[tex]a = 1[/tex]
[tex]b = 12[/tex]
[tex]c = 8[/tex]
[tex]\Delta = {b}^{2} - 4ac[/tex]
[tex]\Delta = {12}^{2} - 4 \times 1 \times 8[/tex]
[tex]\Delta = 144 - 32[/tex]
[tex]\Delta = 112 > 0 = > \exists \: x_{1} \: \neq \: x_{2}\:\in\:\mathbb{R}[/tex]
[tex]x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a} [/tex]
[tex]x_{1,2}=\frac{-12\pm\sqrt{112}}{2 \times 1}[/tex]
[tex]x_{1,2}=\frac{-12\pm4\sqrt{7}}{2}[/tex]
[tex]x_{1,2}=\frac{4(-3\pm\sqrt{7})}{2}[/tex]
[tex]x_{1,2}=2( - 3 \pm \sqrt{7} )[/tex]
[tex]x_{1,2}= - 6 \pm2 \sqrt{7} [/tex]
[tex]x_{1}= - 6 + 2 \sqrt{7} [/tex]
[tex]x_{2}= - 6 - 2 \sqrt{7} [/tex]
