[tex]6 {x}^{2} + 5x + 1 = 0[/tex]
[tex]a = 6[/tex]
[tex]b = 5[/tex]
[tex]c = 1[/tex]
[tex]\Delta = {b}^{2} - 4ac[/tex]
[tex]\Delta = {5}^{2} - 4 \times 6 \times 1[/tex]
[tex]\Delta = 25 - 24[/tex]
[tex]\Delta = 1>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{-5\pm\sqrt{1}}{2 \times 6}[/tex]
[tex]x_{1,2}=\frac{-5\pm1}{12}[/tex]
[tex]x_{1}=\frac{-5 + 1}{12}[/tex]
[tex]x_{1}=\frac{ - 4}{12}[/tex]
[tex]x_{1}= - \frac{4}{12}[/tex]
[tex]x_{1}= - \frac{1}{3}[/tex]
[tex]x_{2}=\frac{-5 - 1}{12}[/tex]
[tex]x_{2}=\frac{- 6}{12}[/tex]
[tex]x_{2}= - \frac{6}{12}[/tex]
[tex]x_{2}= - \frac{ 1}{2}[/tex]
[tex]x_{2} < x_{1} = > - \frac{1}{2} < - \frac{1}{3} [/tex]
