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In this work we demonstrate how one can, in a generic approach, derive a setof $N$ simple quadratic Bethe equations for integrable Richardson-Gaudin (RG)models built out of $N$ spins-1/2. These equations depend only on the $N$eigenvalues of the various conserved charges so that any solution of theseequations defines, indirectly through the corresponding set of eigenvalues, oneparticular eigenstate.  The proposed construction covers the full class of integrable RG models ofthe XYZ (including the subclasses of XXZ and XXX models) type realised in termsof spins-1/2, coupled with one another through $\sigma_i^x \sigma_j^x $,$\sigma_i^y \sigma_j^y $, $\sigma_i^z \sigma_j^z $ terms, including, as well,magnetic field-like terms linear in the Pauli matrices.  The approach exclusively requires integrability, defined here only by therequirement that $N$ conserved charges $R_i$ (with $i = 1,2 \dots N$) such that$\left[R_i,R_j\right] =0 \ (\forall \ i,j)$ exist . The result is thereforevalid, and equally simple, for models with or without $U(1)$ symmetry, with orwithout a properly defined pseudo-vacuum as well as for models with non-skewsymmetric couplings.

Quadratic operator relations and Bethe equations for spin-1/2 Richardson-Gaudin models