Question 295420
Your continuation:
4u+1=0
4u=-1
u=-1/4 not 1/4
u=(x-1)/(x-8)

-1/4=(x-1)/(x-8)
-1*(x-8)=4*(x-1)
-x*8=4x-4
12=5x
12/5=x

or from the beginning
16((x-1)/(x-8))^2+8*((x-1)/(x-8))+1=0
multiply the second term by (x-8)/(x-8)
and 1 by (x-8)^2)/(x-8)^2)
16((x-1)/(x-8))^2+8*((x-1)(x-8)/(x-8)^2)+(x-8)^2)/(x-8)^2)=0
which reduces to
(5x-12)^2/(x-8)^2 = 0
and then to
(5 x-12)^2 = 0
then 
5x-12 = 0
then 5x=12
x=12/5