How can we use Cardano's method to solve a real life problem? I am making a math project for my school. We can make it on any topic, but should involve some college level math. I have chosen 'Cardano's method' as my topic. I will be showing the method to solve a general cubic equation$$ax^3+bx^2+cx+d=0$$ using this method and also show how an example with given coefficients a, b, c and d. The problem is I must also be able to solve a real life problem (even if it's hypothetical) using whatever math I am using. At first I considered the real gas equation:
$$(P+\frac{an^2}{V^2})(V-nb)=nRT$$ On knowing all the parameters except volume, we get a cubic equation is V. I first tried to plus in some real values for oxygen gas, but the equation I received contained very huge numbers and was difficult to solve. I tried considering hypothetical values of Vander Waal's constant a and b and yet it was pretty difficult to solve using cardano's method. Is there a simple real life problem which requires us to find the roots of a cubic equation and gives simple answers?

I won't give you an explicit question, but I suggest you think of problems like this: A right cylindrical cone has base radius $R$ and height $H$. A right circular cylinder of base radius $r$ and height $h$ is inscribed in the cone. Find its dimensions if its volume is a given fraction $c$ times the volume of the cone.
You can think of other geometric problems with cubes inscribed in spheres, etc.
P.S. I'm not sure I consider this college level math; certainly the basics of complex numbers and DeMoivre's formula shouldn't be.
