(x-9)(3x-12)=0

Solution for (x-9)(3x-12)=0 equation:

(x-9)(3x-12)=0

We multiply parentheses ..

(+3x^2-12x-27x+108)=0

We get rid of parentheses

3x^2-12x-27x+108=0

We add all the numbers together, and all the variables

3x^2-39x+108=0

a = 3; b = -39; c = +108;
Δ = b2-4ac
Δ = -392-4·3·108
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-15}{2*3}=\frac{24}{6}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+15}{2*3}=\frac{54}{6}
=9
$