cubic polynomials (ax³+bx²+cx+d) with three real roots can be solved using trigonometry

you can visualize it geometrically with an equilateral triangle

🔵 the vertices align with the roots
🔴 the center with the inflection point
🟢 the incircle boundary with the local min/max pic.twitter.com/doBrGI7pDp

— Freya the stray (@FreyaHolmer) June 18, 2021