I did a short video about symbolic solutions versus numerical methods. The point is that a solution such as

\(x=\left(\frac{\sqrt{5339}}{8\,3^{\frac{3}{2}}}+\frac{379}{216}\right)^{\frac{1}{3}}-\dfrac{2}{9\,\left(\frac{\sqrt{5339}}{8\,3^{\frac{3}{2}}}+\frac{379}{216}\right)^{\frac{1}{3}}}-\dfrac{1}{3}\)

are not helpful, unless you are a number theorist. The solutions of equations of degree 5 are usually not available at all.

This has to be continued, because often symbolic computations can be useful if done in a clever way. Stay tuned.