normal to curve

Question

im currently tutoring and came across this problem however cant seem to get the right answer:

the normal to the curve $2y=3x^3-7x^2+4x$ at the points O$(0,0)$ and A$(1,0)$ meet at the point N

a) find the coordinates of N

Answer 1

1) Differentiate implicitly:

$$2dy=9x^2dx-14xdx+4dx\implies y'=\frac{dy}{dx}=\frac{9x^2-14x+4}2$$

2) Calculate the slope of the tangent line at each point, for example at (0,0):

$$y'(0)=\frac42=2$$

3) Calculate now the normal line of the function at $\;(0,0)\;$ (with slope $\;-\frac12\;$...why?!):

$$y=-\frac12x$$

4) Do (2)-(3) now for the other point $\;(1,0)\;$ and calculate both lines' intersection point.