When, where and **how often** do you find polynomials of higher degrees than two in mathematical, pure/applied, research? A formula for solving a polynomial of degree three, see this link; $ax^3+bx^2+cx+d=0$, is
$$\begin{align}
x\quad&=\quad
      \sqrt[3]{
          \left(
              \frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}
          \right) 
          +      
          \sqrt{
              \left(
                  \frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}
              \right) ^2  
              + 
              \left(
                  \frac{c}{3a} - \frac{b^2}{9a^2}
              \right) ^3 
          }
      }\\
      &+\quad
      \sqrt[3]{
          \left(
              \frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}
          \right) 
          -      
          \sqrt{
              \left(
                  \frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}
              \right) ^2  
              + 
              \left(
                  \frac{c}{3a} - \frac{b^2}{9a^2}
              \right) ^3 
          }
      }
      \;-\;\frac{b}{3a}
\end{align}$$

Unlike quadratic, cubic, and quartic polynomials, the general quintic
  cannot be solved algebraically in terms of a finite number of
  additions, subtractions, multiplications, divisions, and root
  extractions, as rigorously demonstrated by Abel (Abel's impossibility
  theorem) and Galois. However, certain classes of quintic equations can
  be solved [...] Source: http://mathworld.wolfram.com/QuinticEquation.html

At levels of $5^{\text{th}}$ degree polynomials, things are starting to look really serious in my eyes. My question is:

If it is possible to not answer subjectively: When, where and how often do you find polynomials of higher degrees than two in mathematical, pure/applied, research? 


Cubic polynomials are ubiquitous in computer-aided design and computer graphics. 
They also are the basis for computer fonts.
Finite element analysis is based on polynomial functions. Isogeometric analysis uses NURBS. 
