have a 90 x 108 quilt that I want to have quilted.
What size wide backing do I buy????

You'd probably want to buy 3.5 to 4 yards of the 108" wide . That will give you plenty of room (at least 9") on the sides and the ends when you do the quilting.

The 90" can go on the same axis as the 108" or 110" axis of the wide backing. Then you need enough for the 108" side. If you add 8" to that you get 116", so I would just buy 3.5 yards.

When I need to buy backing and can buy a fabric wide enough that I won't need to seam it, it's an easy formula. 108" is wide enough for your 90" side. Then take the other measurement (108") and divide by 36" (1 yard). The answer is 3. 3 yards will be enough for your backing but you need more because the fabric will shift and you don't want to be short at one side, or corner, etc. I'd get 3 1/2 yards.... that will give you 9" extra on each end.... for shifting, etc. And you'll have some scraps for your stash..... Yeah!!