This paper discovers and proves the existence of a general, non-radical-based formulaic solution for the general quintic equation with complex coefficients. The method involves transforming the general form of the equation into a formulaically solvable form—referred to herein as standard form— given by x^5−px+ 1 = 0 , where p is an arbitrary complex number. When the modulus of p satisfies |p|≥1.65, the solution is derived using a series expansion involving negative integer powers with its coefficients of an integral series; conversely, when |p|< 1.65 , a series expansion involving positive powers with its coefficients of a fractional series is employed. These two approaches form a complete and logically closed loop. This method is purely algebraic in nature, requiring neither root searching nor iterative procedures. Furthermore, since any general quintic equation with complex coefficients can invariably be transformed into this standard form, the proposed method possesses universal applicability. Numerical results demonstrate that the method presented in this paper is highly practical and easy to implement.