Help with intersection of two points please :)

1a)
show the points of intersection of
y=x(4-x) and y=x^2(7-x)
are given by the solutions to the equation x(x^2-8x+4)=0 (3 marks)

The point A lies on both of the curves and the x and y coorinates of A are both positive.

b) Find the exact coordintes of A, leaving your answer in the form (p+q root 3, r+s root 3), where p,q,r and s are integers. ( 7 marks)

thanks for any help and can you show clearly your working so that i know how you reached your answer. :)

Sol: x(4-x) = x^2(7 -x)
4x -x^2 = 7x^2 - x^3
x^3- 8x^2+4x = 0
x{x^2 -8x +4} =0.....................Ans
Therefore
x = 0 and y = 0 The point A(0,0)............Ans
and x^2 -8x + 4 = 0
(x^2 -8x +16) +4- 16 =0
(x-4)^2 = 12
taking square root
x = 4 +2(3)^(1/2) and x = 4-2(3)^(1/2)
therefor y = 4 -{4-2(3)^(1/2)} = 2 sqrt(3)
Hence point is { 4-2(3)^(1/2), 2 sqrt(3)}.................Ans