# 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 _{2}x²+a_{1}x+a_{0}=0

a=12a_{1}³-3a_{1}²a_{2}²-54a_{1}a_{2}a_{0}+81a_{0}²+12a_{0}a_{2}³

b=³√36a_{1}a_{2}-108a_{0}-8a_{2}³+12√a

x_{1}=(b²-12a_{1}+4a_{2}²-2a_{2}b)/(6b)

p=(-b²+12a_{1}-4a_{2}²-4a_{2}b)/(-6b)

q=(a_{1}a_{2}b-9ba_{0}+b√a+b²a_{1}-2a_{1}a_{2}²-18a_{2}a_{0}+2a_{2}√a+12a_{1}²)/(3b²)

x_{2}=-p/2+i√-(p/2)²+q

x_{3}=-p/2-i√-(p/2)²+q