# The equation III-th degree

## How do you solve an equation of the third degree with real roots

An equation of the third degree has the form:

To solve this equation we use the following substitution:

Then we have:

, where

,

We note:

The roots of this equation are:

### The Discriminant of the equation

1.  If Δ < 0: The equation has 3 distinct real roots (solutions).

2.  If Δ = 0: The equation has three real roots, of which at least two are the same.

3.  If Δ > 0: The equation has only one real root and two complex roots, combined.

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