There’s the quadratic formula and the one for 3 and 4 factor ones (apologies if I’m wording this wrong), but I just heard that apparently there isn’t anything like a quintic(?) formula and so on. Why is this?? Googling gives me a bunch of confusing terminology that’s difficult to parse.
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The real answer involves [Galois theory](https://math.stackexchange.com/questions/1733072/the-quintic-equation-why-is-there-no-closed-formula), but I’m not sure any 5-year old would understand that. It was apparently too difficult for even the famous mathematician Poisson (of Poisson distribution and Poisson equation fame), who said “”[Galois’s] argument is neither sufficiently clear nor sufficiently developed to allow us to judge its rigor”.
I’ll add that in practice, nobody usually cares, because for a fifth-order polynomial, you are guaranteed at least one real root. You can divide by that root to get a fourth-order polynomial that you could then solve analytically. Or, just keep solving numerically…
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