Calculate a Cubic Equation

Calculator for cubic equations. The three results of the equation ax³+bx²+cx+d=0 will be calculated. Such a third-degree equation always has at least one real solution, but the other two solutions can also be complex numbers. Please enter a value for each coefficient a, b c and d. If this is omitted, then a is set to 1, the others to 0. The formula is converted to normal form so that the parameter a of x³ is 1.
Not for every equation a solution is found!

The solution formulas for cubic equations of the form x³+a₂x²+a₁x+a₀=0 are:
a=12a₁³-3a₁²a₂²-54a₁a₂a₀+81a₀²+12a₀a₂³
b=³√36a₁a₂-108a₀-8a₂³+12√a
x₁=(b²-12a₁+4a₂²-2a₂b)/(6b)
p=(-b²+12a₁-4a₂²-4a₂b)/(-6b)
q=(a₁a₂b-9ba₀+b√a+b²a₁-2a₁a₂²-18a₂a₀+2a₂√a+12a₁²)/(3b²)
x₂=-p/2+i√-(p/2)²+q
x₃=-p/2-i√-(p/2)²+q