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Using an algebraic condition of vanishing discriminant for multiple roots offourth degree polynomials we derive an analytical expression of a shadow sizeas a function of a charge in the Reissner -- Nordstr\"om (RN) metric\cite{Reissner_16,Nordstrom_18}. We consider shadows for negative tidal chargesand charges corresponding to naked singularities $q=\mathcal{Q}^2/M^2 > 1$,where $\mathcal{Q}$ and $M$ are black hole charge and mass, respectively, withthe derived expression. An introduction of a negative tidal charge $q$ candescribe black hole solutions in theories with extra dimensions, so followingthe approach we consider an opportunity to extend RN metric to negative$\mathcal{Q}^2$, while for the standard RN metric $\mathcal{Q}^2$ is alwaysnon-negative. We found that for $q > 9/8$ black hole shadows disappear.Significant tidal charges $q=-6.4$ (suggested by Bin-Nun (2010)) are notconsistent with observations of a minimal spot size at the Galactic Centerobserved in mm-band, moreover, these observations demonstrate that a Reissner-- Nordstr\"om black hole with a significant charge $q \approx 1$ provides abetter fit of recent observational data for the black hole at the GalacticCenter in comparison with the Schwarzschild black hole.

Constraints on a charge in the Reissner--Nordstr\"om metric for the black hole at the Galactic Center