Thanks indeed for everay comments, especially for dharr's commnent. But what I was looking for, is that "Is there any method/s to determine the condition/s on the parameters to have for example two real roots or four real roots, and so on?". I think the Hurwitz criterion gives a sufficient condition for the parameters to all 6 roots to be real, not for example just 2 roots. And another thing I wanted to find is the explicit forms of the solutions. It would be appreciated if someboby help me. Sayed