The shaded region R in the following diagram is bounded by the x-axis, the line y=8x-4 and the curve y=-x^3 + x^2 + 10x + 8

Using technology, or otherwise, find the coordinates of

(i) the point of intersection between the curve and the line
(ii) the point of intersection between the line and the x-axis
(iii) the point of intersection between the curve and the x-axis that is shown in the diagram

Show that the area of region R is equal to exactly 439/12 units squared. Be sure to show all of your work.