I think you are thinking of the Abel–Ruffini impossibility theorum, which states that there is no general solution to polynomials of degree 5 or greater using only standard operations and radicals.
Galois went a step further and proved that there existed polynomials whose specific roots could not be so expressed. His proof also provided a relatively straightforward way to determine if a given polynomial qualified.
Galois went a step further and proved that there existed polynomials whose specific roots could not be so expressed. His proof also provided a relatively straightforward way to determine if a given polynomial qualified.