Sample

The canonical form of cubic equation is

Vieta's formulae are used to solve equations as

thus, first step is to divide all coefficients by "a".

Here is calculator, description of calculation using Vieta's formulae are below

The only place I was able to find Vieta's formulae tailored for cubic equations is here

First we calculate

Then

If S > 0, then

and we have three real roots:

If S < 0, trigonometric functions are replaced with hyperbolic. Depending on sign of Q

Q > 0:

(real root)

(two complex roots)

Q < 0:

(real root)

(two complex roots)

If S = 0, then it is singular equation and has only two roots:

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