Find the largest integer $k$ such that the equation 5x^2 - kx + 8 - 20x^2 + 45 = 0 has no real solutions.
Simplify as
-15x^2 -kx + 53 = 0
This will have no real solutions when the discriminant is < 0
k^2 - (4)(53)(-15) < 0
k^2 + 3180 < 0
k^2 + 3180 is always > 0.....so no value of "k" will give us non-real solutions
+619 
