a; b; c; d = ---
a=0 ?
b=0 ?
D=b.b.b - 3.a.c
D=0 ?
k=b.b.b - 27.a.a.d
k=(9.a.b.c - 2.b.b.b - 27.a.a.d)/ 2/(cub(abs(D))
k=0 ?
x=-b/3/a
x=(-b+cbrt(k))/ 3/b
D<0 ?
x=sqrt(D).(cbrt(k+sqrt(k.k+1)) + cbrt(k-sqrt(k.k+1)))/3/a - b/ 3/a
abs(k)>=1 ?
x=sqrt(D).abs(k).(cbrt(k+sqrt(k.k+1)) + cbrt(k-sqrt(k.k+1)))/3/a/k - b/ 3/a
x1=((2/3.sqrt(D).arccos(k)) - b)/ 3/a
x2=((2/3.sqrt(D).arccos(k)-2pi) - b)/ 3/a
x3=((2/3.sqrt(D).arccos(k)+2pi) - b)/ 3/a
c=0 ?
D=c.c - 4.b.d
D<0 ?
No Solution
D=0 ?
x=-c/b
x1=(-c+sqrt(D))/ 2/b x2=(-c-sqrt(D))/ 2/b
THUẬT TOÁN GIẢI TỔNG QUÁT PHƯƠNG TRÌNH: ax^3 + bx^2 + cx + d = 0
d=0 ?
x=-d/c
Infinite Solutions
No Solution