How many points are in the intersection

How many points are in the intersection of y = x2 + 3x + 1 and y = 2x + 5?

Please show me how to solve this step-by-step! Thank you :)

to find intersection
set


x^2 + 3x + 1=2x+5
or
x^2 + x -4=0

x=(-1+sqrt(1+4*4))/2

x=(-1-sqrt(1+4*4))/2

answer two intersection points
x=(-1+sqrt(17))/2 y=4+sqrt(17)
or
x=(-1-sqrt(17))/2 y=4-sqrt(17)

set the two functions equal to each other.

x^2+3x+1=2x+5

x^2+x-4=0
[-1+/-sqrt(1+4)]/2.
There are two intersection points.