Solving a Quartic Function – Mathematics Stack Exchange

A user named ‘Uzdawi’ from another post asked a question about how to solve the quartic function of

formula

One of the responses included an answer from the user ‘Peđa Terzić’, which is as follows:

formula

Could anyone kindly elaborate on the method used to get to the answer please.

And how the same method could be used to solve the following function:

formula

If not the same method used by Peđa Terzić, how else could you approach to solving a quartic function?

Thank you for your time.