Math Is Fun Forum

Hi! Does anyone know how to find solutions to polynomials of third degree that can be irrational or not whole numbers? I'm studying for a math competition on which I cannot use a calculator or anything of that sort, and since there is a limited amount of time, I would not like to use plug-and-chug. This is like for those were rational roots theorem  does nothing, and Newton-Raphson is too complicated without a CPU. Thank y'all so much !!!