For an integer n, the inequality x^2 + nx + 15 < -21 - 7x + x^2 has no real solutions in x. Find the number of different possible values of n.
x^2 + nx + 15 < -21 -7x + x^2 simplify as
(n + 7)x < -36
This will have no real solution if n = -7
+24 
