Finding a root of polynomial equations is one of basic problems in mathematics. And Galois theory restricts the general radical solution for the degree no higher than four. The series solution, besides the iterated, is regarded as final and universal method to general polynomial equations. This paper reports a discovery of the standard form of polynomial equations and a class of integer sequences associated thereof, which is a kind of extended Catalan numbers. The solution of polynomial equations in the standard form has a precise and perfect series expression. The convergence condition of the series is clear. For the general polynomial equations which may not be satisfied with the convergence condition, some proper transformations, like the Tschirnhaus transformation can be employed to guarantee the convergence. Considering that up to the quintic, there definitely exists a normal form for general equations, and the normal form can easily be changed to the standard form, our method has established a general, universal and effective technique to the quintic, as well as the quartic, the cubic, and the quadratic, without the radicals.