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In this paper, we design two inertial iterative methods involving one and two inertial steps for investigating a general quasi-variational inequality in a real Hilbert space. We establish an existence result and a non-trivial example is furnished to substantiate our theoretical findings. We discuss the convergence of the inertial iterative algorithms to approximate the solution of a general quasi-variational inequality. Finally, we apply an inertial iterative scheme with two inertial steps to investigate a delay differential equation. The results presented herein can be seen as substantial generalizations of some known results.