If 2x^2 - 5x + k - 6 has no real roots, what are the values of k

b² - 4ac < 0
(-5)² - 4(2)(k - 6) < 0
25 - 8k + 48 < 0
-8k + 73 < 0
-8k < -73
k > 73/8

If it has no real roots, the discriminant b^2 - 4ac is less than 0.

a = coefficient of x^2 = 2
b = coefficient of x = -5
c = constant term = k - 6

So (-5)^2 - 4*(2)(k - 6) < 0

Solve that inequality for k.