# Quartic with complex coefficients

I am trying to solve a fourth order polynomial which is in the following form

$$x^4+Ax^3+(B_1+B_2p)x^2-(C+Ap)x+D+Ep=0$$

Where $$A$$, $$B_1$$, $$B_2$$, $$C$$, $$D$$, $$E$$, are real parameters and p is a complex parameter.

I have investigated many ways of solving this equation however there does not seem to be much information regarding complex coefficients. My solution is very messy for real coefficients but it still exists and I derived it using Ferrari's method. I am not sure if I can use this method in the case where p is complex.

Any suggestions will be much appreciated.