<p>This paper presents a novel iterative algorithm of inertial type for solving equilibrium problems in real Hilbert spaces. The proposed method is derived from the golden ratio algorithm and incorporates an inertial extrapolation mechanism to accelerate convergence. Under standard assumptions, we prove the weak convergence of the sequence generated by the algorithm, thereby ensuring its theoretical validity. We extend the proposed framework to various problem classes, including variational inequalities, fixed-point formulations, LASSO optimization, compressed sensing, and image reconstruction, as applications. Through numerical experiments, we demonstrate the effectiveness of the method, highlighting its superior performance and computational efficiency compared to several existing approaches in the literature.</p>