Find the largest integer k such that the equation 5x^2 - kx + 8 - 20x^2 + 45 = 0 has no real solutions.
Rewrite as
-15x^2 -kx + 53 = 0
This has no real solutions when the discriminant is < 0
k^2 - (-15)(4)(53) < 0
k^2 + 3180 < 0
The discriminant is never < 0 so no k produces non-real solutions
+921 
