This article provides a review that examines the mathematical principles that underlie the three numerical approaches that are utilized the most frequently for the purpose of solving nonlinear equations. For the purpose of demonstrating the numerical estimation of the non-linear equation f(x)=x^3-2x-5, the methods of Bisection, Newton-Raphson, and Secant are utilized. Using the Python programming language, the research investigates and analyzes a number of different tactics based on their capacity to get closer to the actual root of the function with each iteration (convergence). The Newton-Raphson and Secant methods produce more precision and faster convergence with a limited number of iterations, whereas the Bisection approach takes a substantially higher number of iterations to achieve convergence. Both of these methods achieve convergence more quickly and with greater accuracy. In order to arrive at an accurate determination of the root value of 2.09455, the Bisection strategy managed to achieve convergence at the thirteenth iteration, whilst the Newton-Raphson and Secant approaches were able to achieve convergence at the seventh and fourth iterations, respectively. As a result of analyzing three different approaches, it was determined that the Secant method is the most efficient one. On the other hand, the Newton-Raphson method converges more quickly but has a more challenging extraction process.