6x² = x + 2
Subtracting x and 2 at both sides:
6x² - x - 2 = x + 2 - x - 2
6x² - x - 2 = 0
where
a: 6
b: -1
c: -2
Substituting these values into the quadratic formula:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_{1,2}=\frac{1\pm\sqrt[]{(-1)^2-4(6)(-2)}}{2(6)} \\ x_{1,2}=\frac{1\pm\sqrt[]{49}}{12} \\ x_1=\frac{1+7}{12}=\frac{2}{3} \\ x_2=\frac{1-7}{12}=-\frac{1}{2} \end{gathered}[/tex]