I think you'll find that three yards is certainly not enough to make a backing for an 86 x 86 quilt.
If you are sure you want to piece a backing rather than find a wide fabric, this graphic might help.
You'll need TWO lengths of fabric each cut 2 & 5/8 yards long, with an insertion strip at least 7-8" wide x 2 & 5/8 yards long.
Jan in VA
*The piecing is turned this way to give the straight grain of the fabric to the sides of the quilt, in case you ever choose to hang it.*