When B is a value, there is one intersection point between the primary function y = 5x + B and the secondary function y = x ^ 2 + 3x + 5, two intersections and no intersection point?

When B is a value, there is one intersection point between the primary function y = 5x + B and the secondary function y = x ^ 2 + 3x + 5, two intersections and no intersection point?

Is there any intersection between the first function y = 5x + B and the second function y = x ^ 2 + 3x + 5
Let 5x + B = x ^ 2 + 3x + 5
x^2-2x+5-b=0
There is an intersection point when △ = 4-4 (5-b) = 0
That is, there is an intersection point when B = 4
When △ = 4-4 (5-b) > 0, there are two intersections
When b > 4, there are two intersections
△=4-4（5-b)