Solve x^3+px+q=0 in terms of p and q

Question

This is for a math lab question

Could you write I out the steps

Answer 1

x = (-q/2 +(q^2/4 +p^3/27)^.5)^(1/3)

use the cubic formula with a=1, b=0, c=p, d=q

it's not well known, google it

with b=0 it greatly simplifies to

the cube root of (-half q +square root of (q^2/4 + p^3/27))