Question: How to solve a cubic assuming discriminant condition?

Hi MaplePrimes. 

I have a cubic with some parameters that I would like to solve and recieve 3 real solutions, however I cannot seem to find a way to get that to work while using assumptions. I always recieve 1 real and two complex conjugate answers. I have tried assuming the discrimant to be greater then zero but nothing seems to be working, and I have looked through a few posts on here but I cant seem to find anything out. In particular solve({f,conditions},{variable}) 

If I solve with a known set of paramters(which i determine graphically) that gives three solutions everything works fine. Also if I solve the cubic generally and recieve the two complex solutions and one real then substitute the paramters in I get the same correct answers, so I am slightly baffled. If I have missed something simple my apologies. 

Any help would be greatly appreciated. File attached. 

CubicSolve.mw