I need to hang a bookcase (43" x 36") to a wall in my kid's room and for design reasons, didn't plan on a french cleat (and it's too late to add one). Instead I attached stretchers between the sides under two shelves, glued and screwed (with plugs). I assume the unit will carry a fair amount of weight since it is expected to hold junior's books .

My plan is to use either long course thread drywall screws or small diameter lags into the studs, but I'm starting to worry about the strength of this approach. (I guess, now that I think about it, using a FC which is lagged or screwed into the wall would provide roughly the same degree of shear strength, but I want to be sure. I suppose I could just add a decorative supporting cleat below the unit for additional strength.) Any suggestions or have I just answered my own question?

Thanks,