This calculator will find the values of x

_{1}, x_{2}, and x_{3}for a given cubic equation with the following form:**ax**

^{3}+ bx^{2}+ cx + d = 0Simply enter the values for

*a*,*b*,*c*, and*d*below and then click the “Calculate” button.x_{1}: **-0.72932**

x_{2}: **-0.03534 + i * 0.73973**

x_{3}: **-0.03534 – i * 0.73973**

**Explanation:**

**f** = ((3c/a) – (b^{2}/a^{2})) / 3 = 0.38667

**g** = (((2b^{3})/(a^{3})) – (9bc/a^{2}) + (27d/a)) / 27 = 0.27793

**h** = (g^{2}/4) + (f^{3}/27) = 0.02145

**R** = (-g/2) + h^{1/2} = 0.00750

**S** = R^{1/3} = 0.19576

**T** = (-g/2) – h^{1/2} = -0.28543

**U** = T^{1/3} = -0.65841

**x _{1}** = (S+U) – (b/3a) = -0.72932

**x _{2}** = -(S+U)/2 – (b/3a) + i*(S-U)*(3)

^{1/2}/2 = -0.03534 + i * 0.73973

**x _{3}** = -(S+U)/2 – (b/3a) – i*(S-U)*(3)

^{1/2}/2 = -0.03534 – i * 0.73973