Answer: \(y = \dfrac{-1 + \sqrt{73}}{6}\) or \(y = \dfrac{-1 - \sqrt{73}}{6}\)
\(y^2 + \dfrac{1}{3}y - 2 = 0\). Multiplying by 3 : \(3y^2 + y - 6 = 0\).
\(a = 3\), \(b = 1\), \(c = -6\).
\(b^2 - 4ac = 1 - 4(3)(-6) = 1 + 72 = 73\)
\(y = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \dfrac{-1 \pm \sqrt{73}}{6}\)
So \(y = \dfrac{-1 + \sqrt{73}}{6} \approx 1.26\) or \(y = \dfrac{-1 - \sqrt{73}}{6} \approx -1.59\).