This is an extremely simple and efficient solver of algebraic equation of 4th order. I have read so many relating articles, I have tested other solutions... However, this solution contains the algebraic improvement which simplifies things, significantly. 
Consequently, the numerical computations are reduced and as far as I can see, it performs extraordinarily! The theory and mathematical background are explained in the file - theorymath_eng.docx.
The solution of a given quartic equation - x^4 + a·x^3 + b·x^2 + c·x + d = 0 - can be found by the function:
solve_quartic(double a, double b, double c, double d)
The quartic equations may have different types of roots. a) 4 real roots b) 2 real and 2 complex-conjugate roots c) 4 complex roots (two pairs of complex-conjugates). Our solve_quartic() returns the array of four complex numbers. If there are real roots, the immaginary parts of corresponding solutions (array members) will be simply - 0.
(main.cpp file is given here just for testing and experimenting)