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azepoi
I can recommand this video on the subject: Mathologer -- 500 years of NOT teaching THE CUBIC FORMULA. What is it they think you can't handle? https://www.youtube.com/watch?v=N-KXStupwsc
okintheory
As a working applied mathematician, I can tell you it's with pretty good reason. I learnt this stuff in high school and never used it since. It is one of the least useful things you could imagine. It is fun, though.
pdm55
One never knows when one might need a particular bit of mathematics. I wrote a mathematical model of DNA transcription events inside E. coli, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5425810/. For this, I needed the solution to a cubic equation. Thankfully, Cardano had published the solution in the 15th century, and Wang had shown which was the relevant root in more recent times, https://febs.onlinelibrary.wiley.com/doi/epdf/10.1016/0014-5...
chongli
Why not use Newton’s method? Your computer is using numerical approximations for computing those roots anyway. The reason the cubic formula isn’t used is because it’s very convoluted and it doesn’t solve any problems you couldn’t solve with Newton’s method, unless you’re doing algebra and you need an exact solution.
q_revert
exact analytical solutions are nice as a check against any numerical solutions imo. (checking the same calculations in multiple ways is handy for error catching ime)
blondin
first is italian :) hn will bash me for saying but the name reminds me of a pasta brand or name
perl4ever
Trivia from googling:

Tartaglia comes from tartagliare, meaning to stutter.

"Tartaglia was not the family name. Tartaglia took it as a nickname, which referred to his inability to talk clearly as a result of terrible wounds to his head and jaw during the sack of Brescia in 1512"

http://galileo.rice.edu/Catalog/NewFiles/tartalia.html