Okay, I know this question sounds dumb but please hear me out. I need to use the cubic formula (not Cardano's method) the one here: https://math.vanderbilt.edu/schectex/courses/cubic/ and explain that a cubic formula does exist. I tried plugging in the coefficients from a cubic equation for around 3 hours now and I just can't figure it out.
For example, let's say I used an online calculator and found that the roots are 3, 2, and -1. I plug in the coefficients of the same equation into the formula and I get these crazy imaginary numbers impossible to simplify and take out of the cube roots. How is this happening?
My last question is, once you do find x, how do you find the two other answers? I know there is something called the complex numbers or something but I forgot a lot about it.
I really would like to know this and I can't find any step by step guides online. I really hope to find some answers and help here.