Are there formulas to find roots of n-th degree polynomials?

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I have tried a polynomial equation of 7th degree on WolframAlpha but it didn't give me exact forms. Does this mean there are not general formulas for every polynomial equation and calculators use root-finding algorithms?

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The quadratic formula is more famous than its cubic and quartic counterparts, but all three are solutions in radicals, and we can't do the same for higher degrees.