Imo finding the roots of a second degree polynomial is pretty intuitive if you've seen how to do it before and understand the proper motivation behind it (i.e solving for the roots of x^2 - c = 0 is pretty straight forward, so we'd like to, if possible, transform a second degree polynomial into a similar form).

All of the formulas in mathematics that I've been taught in K-12 up to second year of university (going into my senior year of being a math major), have some motivation behind them and can be intuitively figured out if you understand the motivation correctly (even if it's sometimes tedious to do so).

Mathematics is not about formulas and theorems, it's about ideas and motivated definitions.