Trying with rational factors of 2/3 - does not give us a root. This equation has irrational roots.
We reduce the equation by the following method.
Let a = 3, b = -1, c = -8 , d = -2
Substitute y = x + b/3a ie., y = x -1/9
You will get
We follow the above when p is positive in reduced cubic equation. If p is negative in the reduced cubic equation then we do the following. Otherwise, we have work with complex roots. It becomes difficult to evaluate roots.