How do the calculators solve the equations like ax³+bx²+cx+d=0? Is there any specific formula of it? If yes, what's the formula?

You could build on this idea https://code.sololearn.com/c0MP4vcriFf5

Which calculator? A code or a Casio scientific model? Tho this question doesn't seem to be programming related (if it is something about the math.h header file or something, then I'm sorry). You don't need a calculator. They just make you more dependent on others. Solve them by yourself. Stack exchange- the best community. https://math.stackexchange.com/questions/2326445/how-does-my-calculator-calculate-the-roots-for-a-cubic-polynomial#:~:text=So%2C%20given%20any%20two%20numbers,solution%20x%3Du%2Bv.&text=From%20%E2%88%923uv%3Db,quadratic%20equation%20in%20u3.

I dont know what language calculators are written in (assembly or C I would guess), and I dont know the formula. But I think if you know how polynomials work and how they are solved, it wouldnt be too hard to write code that solves them.