Find the largest integer $k$ such that the equation 5x^2 - kx + 8 - 12x^2 + 87 = 0 has no real solutions.
Simplify as
-7x^2 - kx + 95 = 0
If this has no real solutions, the discriminant < 0
k^2 - 4(-7) (95) < 0
k^2 + 2660 < 0
No integer k makes this true
+1459 
