[tex]4 {x}^{2} - 12x + 8 = 0[/tex]
[tex]a = 4[/tex]
[tex]b = - 12[/tex]
[tex]c = 8[/tex]
[tex]\Delta = {b}^{2} - 4ac[/tex]
[tex]\Delta = {( - 12)}^{2} - 4 \times 4 \times 8[/tex]
[tex]\Delta = 144 - 128[/tex]
[tex]\Delta = 16 > 0 = > \exists \: x_{1} \: \neq \: x_{2}[/tex]
[tex]x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a}[/tex]
[tex]x_{1,2}=\frac{-( - 12)\pm\sqrt{16}}{2 \times 4} [/tex]
[tex]x_{1,2}=\frac{12\pm4}{8} [/tex]
[tex]x_{1}=\frac{12 + 4}{8} [/tex]
[tex]x_{1}=\frac{16}{8} [/tex]
[tex]x_{1}=2[/tex]
[tex]x_{2}=\frac{12 - 4}{8} [/tex]
[tex]x_{2}=\frac{8}{8} [/tex]
[tex]x_{2}=1[/tex]
