Where does the line y= 5x-3 meets the curve f(x) = x^2 +3 ?

Given the line y= 5x -3 and the curve f(x) = x^2
+3

We need to find the intersection points between the line and the
curve.

==> f(x) = y

==>
x^2 + 3 = 5x-3

==> Now we will combine like
terms.

==> x^2 - 5x + 6 = 0

Now
we will factor.

==> (x-3)(x-2) =
0

==> x 1= 3 ==> y1 = 5x-3 = 5*3-3 =
12

==> x2= 2 ==> y2= 5x-3 = 5*2-3 =
7

Then the intersection points are ( 2,7) and (3,
12)