Root-finding in nonlinear equations is a fundamental problem in numerical analysis with applications in mathematics and engineering. Traditional methods like the Bisection and False Position methods have been widely used, but they often face challenges related to convergence speed, stability, and computational efficiency. This paper presents two novel numerical root-finding methods that combine the robustness of the Bisection method with the efficiency of the False Position method, improving both convergence rates and stability. Furthermore, we illustrate some numerical applications to discuss error analysis, convergence analysis, and comparisons with existing methods. These findings contribute to the advancement of numerical computation by providing more reliable and efficient root-finding techniques.