  We provide quantitative inner and outer bounds for the symmetric quasiconvex
hull $Q^e(\mathcal{U})$ on linear strains generated by three-well sets
$\mathcal{U}$ in $\mathbb{R}^{2\times 2}_{sym}$. In our study, we consider all
possible compatible configurations for three wells and prove that if there
exist two matrices in $\mathcal{U}$ that are rank-one compatible then
$Q^e(\mathcal{U})$ coincides with its symmetric lamination convex hull
$L^e(\mathcal{U})$. We complete this result by providing an explicit
characterization of $L^e(\mathcal{U})$ in terms of the wells in $\mathcal{U}$.
Finally, we discuss the optimality of our outer bound and its relationship with
quadratic polyconvex functions.
