I've got an equation: 4x^3 - 24x^2 + 45 x - 23

A tangent is drawn at point P. (1,2)

dy/dx = 12x^2 - 48x +45

At f´(1) = 12 -48 + 45 = 9

2 = 9(1) +c

y = 9x - 7

Show that the x coordinate of point q is 4.

9x-7 = 4x^3 - 24x^2 + 45 x - 23

0 = 4x^3 - 24x^2 + 36 x - 16

I found x = 4 using polyrootfinder on my gdc and was wondering if there is any other way of coming to that answer?