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

Solution for (3x-9)(x-9)=0 equation:

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

We multiply parentheses ..

(+3x^2-27x-9x+81)=0

We get rid of parentheses

3x^2-27x-9x+81=0

We add all the numbers together, and all the variables

3x^2-36x+81=0

a = 3; b = -36; c = +81;
Δ = b2-4ac
Δ = -362-4·3·81
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-18}{2*3}=\frac{18}{6}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+18}{2*3}=\frac{54}{6}
=9
$