(x-4)(3x-9)=0

Solution for (x-4)(3x-9)=0 equation:

(x-4)(3x-9)=0

We multiply parentheses ..

(+3x^2-9x-12x+36)=0

We get rid of parentheses

3x^2-9x-12x+36=0

We add all the numbers together, and all the variables

3x^2-21x+36=0

a = 3; b = -21; c = +36;
Δ = b2-4ac
Δ = -212-4·3·36
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3}{2*3}=\frac{18}{6}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3}{2*3}=\frac{24}{6}
=4
$