how did Cardano obtain three solutions for cubic? So, if I am not mistaken Complex numbers were discovered after Cardano's method. But from Cardano's Method on Wikipedia, it says to get the three solutions, we should use the root of unity. In that case, when Cardano's method was published it could only find one solution?  

The method of solving a cubic is explained very clearly in Stroud's Further Engineering Mathematics.  According to Stuart Hollingdale's book "Makers of Mathematics", Cardano plagiarized Tartaglia's solution of the cubic.  Paul Halmos said that he solved this problem for himself as a high school student.
