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Hi, in quasi-static case we should ideally be solving KU = F.
However, in some highly nonlinear cases, it may be difficult to obtain convergence by using an implicit solver. In such cases, one workaround is to use the explicit solver and solve KU + MA = F (explicit solver cannot be used to solve KU = F, it can only be used to solve KU + MA = F), but ensure that the loading is such that kinetic energy is a very small percentage of the total energy. Then, although you are not solving a static case, because the kinetic energy is low, it can be considered to be quasi-static.
So based on the case and what solver is being used to model the quasi-static case, one can solve either KU=F or KU + MA = F equation.