You have my sympathy. The 2010 to 2013 Equinox 2.4 4 cyl had oil consumption issues due to premature wear of the piston oil control rings. This thread is about the same problem I had with my 2013 Equinox.
GM was replacing the rings and pistons under an extended warranty, you need to check if your Equinox qualifies.
Good luck,
Ed B.