#### Answer

$x=\dfrac{3}{2}\pm\dfrac{\sqrt{11}}{2}$

#### Work Step by Step

$\dfrac{1}{3}y^{2}-y-\dfrac{1}{6}=0$
Multiply the whole equation by $6$ to avoid working with fractions:
$6\Big(\dfrac{1}{3}y^{2}-y-\dfrac{1}{6}=0\Big)$
$2y^{2}-6y-1=0$
Use the quadratic formula to solve this equation. The formula is $y=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=2$, $b=-6$ and $c=-1$
Substitute:
$y=\dfrac{-(-6)\pm\sqrt{(-6)^{2}-4(2)(-1)}}{2(2)}=\dfrac{6\pm\sqrt{36+8}}{4}=...$
$...=\dfrac{6\pm\sqrt{44}}{4}=\dfrac{6\pm2\sqrt{11}}{4}=\dfrac{3}{2}\pm\dfrac{\sqrt{11}}{2}$