  Using a continued fraction ansatz we obtain an analytic approximation for a
spherically symmetric black hole solution to Einsteinian Quartic Gravity (EQG),
the next simplest Generalized Quasi-Topological Gravity (GQTG) after
Einsteinian Cubic Gravity (ECG). This approximate solution is valid everywhere
outside of the horizon and we use it to investigate the orbit of massive test
bodies near a black hole, specifically computing the innermost stable circular
orbit. Using Shapiro time delay we calculate the constraints on the EQG
coupling parameter. Finally we compute the shadow of an EQG black hole and
figure out it to be larger than its Einsteinian counterpart in general
relativity for the same value of the mass. By applying our results to
Sagittarius A* (Sgr A*) at the center of Milky Way we find, similar to ECG
black holes, that departures from general relativity are small but
distinguishable for EQG black holes.
