If a, b, c, and d are different integers, find the value of a+b+c+d

x-a,x-b,x-c,x-d,can have the values 5,1,-5,-1.

x=7 implies that a,b,c,d,can have values 2,6,12,8.

Therefore,a+b+c+d=2+6+12+8=28.

Voila!