The impact of load sharing between the electric vehicles (EVs) aggregator and the conventional generator on stability delay margins in a two-area load frequency control (LFC) system is investigated in this work. A frequency-domain Rekasius substitution method is used to compute stability delay margins for different values of proportional-integral (PI) controller gains. The proposed method computes complex roots on the imaginary axis of the quasi-characteristic equation. The substitution first converts the quasi-characteristic equation of the LFC with EVs aggregator (LFC-EVs) system including delay-dependent exponential terms into an ordinary polynomial. Then, the Routh-Hurwitz stability method is applied to find those imaginary roots and the corresponding stability delay margins. The qualitative impact of different sharing schemes between the conventional generator and EVs aggregator and the impact of EVs gains on stability delay margins are thoroughly analyzed, and the results are validated by time domain simulations and quasi-polynomial mapping-based root finder algorithm. It is observed that for any given PI controller gains, stability delay margins decrease when the participation of EVs into the frequency regulation increases.