When to resort to numerical methods when solving one variable equations?

Hello. I have learning numerical methods on my own. The first chapter, which revolves around solving equations with a single variable, numerically raised a question in my head. How do I know when an equation can be solved analytically or when an equation is simply unsolvable (Like as Abel-Ruffini theorem explains, if a polynomial is of 5th order or higher, there is no analytical formula directly) or difficult to solve (oftentimes trigonometric ones, I suppose), so I can decide when to resort to numerical methods?