3(x-9)(x-9)=81

Solution for 3(x-9)(x-9)=81 equation:

3(x-9)(x-9)=81

We move all terms to the left:

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

We multiply parentheses ..

3(+x^2-9x-9x+81)-81=0

We multiply parentheses

3x^2-27x-27x+243-81=0

We add all the numbers together, and all the variables

3x^2-54x+162=0

a = 3; b = -54; c = +162;
Δ = b2-4ac
Δ = -542-4·3·162
Δ = 972
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-18\sqrt{3}}{2*3}=\frac{54-18\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+18\sqrt{3}}{2*3}=\frac{54+18\sqrt{3}}{6}
$