I was reading about quintic equations and this came up:
In the early nineteenth century, Paolo Ruffini (1765–1822) and Niels Henrik Abel (1802–1829) proved that no such general formulas utilizing the usual operations and root operations exist. This means that there will never be a simple formula that provides the solutions for every single a, b, c, d, e, and f in a quintic equation.
so, I am a little confused. isn't the goal of solving a quintic equation is to find X? what is the role of coefficients in here? can anyone explain?