I'm helping my son with Math in high school. He is now learning to solve higher order equations, with for example $x^4$, $x^3$ or $x^5$. The point is that he sees no use in solving these equations (apart from an algebraic challenge) because for him they serve no purpose.
The quadratic equation is easy to illustrate by applying it to a ball you throw upward.
Would you have some examples of real-life systems where higher order equations are used?
Tks!