(9x-81)(x-9)=1

Solution for (9x-81)(x-9)=1 equation:

(9x-81)(x-9)=1

We move all terms to the left:

(9x-81)(x-9)-(1)=0

We multiply parentheses ..

(+9x^2-81x-81x+729)-1=0

We get rid of parentheses

9x^2-81x-81x+729-1=0

We add all the numbers together, and all the variables

9x^2-162x+728=0

a = 9; b = -162; c = +728;
Δ = b2-4ac
Δ = -1622-4·9·728
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-6}{2*9}=\frac{156}{18}
=8+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+6}{2*9}=\frac{168}{18}
=9+1/3
$