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Please note that there may be other methods apart from this large formulas to solve cubics and quartics. But I wanted to show here that the formulas do exist.

The general form of the 3rd degree equation (or Cubic) is: ax3 + bx2 + cx + d = 0

Cubics have 3 roots.

The 3 roots can be represented this way:

F irst root (of three):

Second root (of three):

Third root (of three):

The second and third formula are equal except for a "+ or -" sign at the beginning, and another "+ or -" sign in the middle. Note that the second and third formula contain the imaginary unit "i".





Now, the same three formulas in ASCII. The differences between the second and third formula are highlighted here in yellow: