Math problem: Solving cubic equation

Source expression:

Moving the right part of the equation:

Raising the expression to power:

Collecting terms:

It is a cubic equation

The equation looks like:

where:

Let us solve the equation using the Cardano-Vieta method

Let us calculate the coefficients:

The equation has 1 real root and 2 complex roots because

Let us calculate the roots of the equation using the Cardano formulas: