The quintic was almost proven to have no general solutions by radicals by Paolo Ruffini in 1799, whose key insight was to use permutation " groups ", not just a single permutation.
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The Abel Ruffini theorem states that such a solution by radicals does not exist, in general, for equations of degree at least five . �variste Galois showed that an equation is solvable in radicals if and only if its Galois group is solvable.
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And to Bo Jacoby, yes the formula is basically useless, but if someone wants to solve a'poorly behaved'Quartic by hand, and they want a solution by radicals, they often follow something like Ferrari's method through w / number in place of those unwieldy expressions, correct ? talk ) 20 : 23, 30 July 2009 ( UTC)
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