You asked if cubic equations were of use in real life. They are. The equation of state describing a real gas is usually in the form of a cubic equation. The names of some are Van Der Waals, Redlich-Kwong and Peng-Robinson. They are all solved for the z the compressibility of the gas. The solutions are real and between 0 and 1. The smallest solution describes the z attributed to the liquid phase. The largest z is the gas phase. Certain other equations describe the liquid vapor equilibrium and use z the solution of the cubic equation to do so. They also describe the Enthalpy of the gas under various conditions.
Check in the Chemical Engineering Forum for the use of Cubic Equations. Here is one posted.
Check in the Chemical Engineering Forum for the use of Cubic Equations. Here is one posted.