Answer
$x=${$\dfrac{3 \pm \sqrt{11}}{2}$}
Work Step by Step
Given: $\dfrac{x^2}{3}-x-\dfrac{1}{6}=0$
Re-write the equation as: $2x^2-6x-1=0$
Factorize the expression with the help of quadratic formula. Quadratic formula suggests that $x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$
This implies that $x=\dfrac{-(-6) \pm \sqrt{(-6)^2-4(2)(-1)}}{2(2)}$
or, $x=\dfrac{6 \pm \sqrt{44}}{4}$
or, $x=\dfrac{6 \pm 2\sqrt{11}}{4}$
Hence, our solution is:
$x=${$\dfrac{3 \pm \sqrt{11}}{2}$}
