Find the largest number $c$ such that the quadratic equation $2x^2+5x+c=x^2+7x$ has at least one real solution.
2x^2 + 5x + c = x^2 + 7x rearrange as
x^2 - 2x + c = 0
This will have at least one real solution when the discriminant ≥ 0
So
(-2)^2 - 4(1)(c) ≥ 0
4 - 4c ≥ 0
4 ≥ 4c
1 ≥ c
So....it will have at least one real solution when c ≤ 1
+721 
