Relativity is directly recovered. In the present considerably longer paper, we are now giving the details of the derivation summarized in [@PodolskySvarcPravdaPravdova:2018], and also survey and analysis of other classes of spherically symmetric solutions to Quadratic Gravity.

Our paper is organized as follows. In Sec. \[QGandEWtheory\] we recall the Quadratic Gravity and the Einstein–Weyl theory, and we put the corresponding field equations into a convenient form in which the Ricci tensor is proportional to the Bach tensor. In Sec. \[BHmetricsec\] we introduce a suitable spherically symmetric metric ansatz in the conformal-to-Kundt form, and we give relations to the standard metric form. In Sec. \[derivingFE\] we overview the derivation of the field equations with various technical details and thorough discussion being postponed to Appendices A–C. In Sec. \[invariants\] expressions for curvature invariants are derived. In Sec. \[integration\] expansions in powers of ${\Delta \equiv r-r_0}$ around a fixed point $r_0$, and for $r \rightarrow \infty$ are introduced. In Sec. \[expansiont\_0\] the leading orders in ${\Delta }$ of the field equations are solved and four main classes of solutions are obtained. For these solutions, in Sec. \[description\] all coefficients of the metric functions in the power expansions in $\Delta$ are given in the 