if yo meant 4x^2-2x+6=0
you would get x=something and x=something
those line are up and down
(x,y)
given
(2,3)
the line is x=2
but, if yo meant
4x^2-2x+6=y
find the slope at the point where x=2
take the derivitive
8x-2=dy/dx
at x=2
8(2)-2=dy/dx
16-2=dy/dx
14=dy/dx
the slope at (2,3) is 14
point slope form
the equation of a line going through (x1,y1) and the slope is m is
y-y1=m(x-x1)
given
(2,3)
m=14
y-3=14(x-2)
y-3=14x-28
add 3 both sides
y=14x-25
minus 14x both sides
-14x+y=-25
times -1 (x term is normally positive)
14x-y=25
