The primary objective of this research is to discover the ideal way to solve the non-linear equation using iterative methods. This article examines and highlights the four iterative methods to dealing with non-linear equations. As a consequence of this approach, the pace of convergence between first-degree iterative procedures is explained. The graphical development is then built up utilizing the four iterative methods and the outcomes are evaluated using different functionalities. An example of the algebraic equation is presented to compare the approximation inaccuracy among the methods. In addition, two examples of algebraic and transcendental equations are utilized to verify both the optimum method and the extent of the visibly presented errors.