At what point does the curve y = 3x^2 - 5x + 3 meet the line y= x.

Given the curve 3x^2  5x + 3 and the line y=
x

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

The points of intersections are the points
that verifies the following.

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

Let us move x to the left
side.

==> 3x^2 - 6x + 3 =
0

Now we will divide by
3.

==> x^2 - 2x + 1 =
0

Now we will
factor.

==> (x-1)(x-1) =
0

==> x = 1

==>
y= 1

Then the point of intersection is
(1,1)