The domains of engineering, physics, chemistry, biosciences, and many more find it in several real-world scenarios. An implicit uncertainty in a scientific or engineering equation really creates a root-finding issue. Furthermore, two numerical methods for addressing root-finding problems in nonlinear equations with the presumption of a solution have been discussed, in addition to the bisection technique and the Newton-Rhapson method. Many of these iterative methods are really multi-stage iterative processes including predictor and corrector stages. Computational mathematics is a branch of mathematics concerned with the development and use of mathematical models, algorithms, and procedures for the goal of solving complex problems in many different academic domains, such as science, engineering, finance, and others. An algorithm is just a set of rules on how to do something. Finding the roots of the mathematical function is now possible using techniques such as the Newton-Raphson method. An essential use of computational mathematics is its integration with scientific investigation. By simulating real-world events in virtual environments, researchers may study how natural systems function.