(3x-12)(4x-8)=0

Solution for (3x-12)(4x-8)=0 equation:

(3x-12)(4x-8)=0

We multiply parentheses ..

(+12x^2-24x-48x+96)=0

We get rid of parentheses

12x^2-24x-48x+96=0

We add all the numbers together, and all the variables

12x^2-72x+96=0

a = 12; b = -72; c = +96;
Δ = b2-4ac
Δ = -722-4·12·96
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-24}{2*12}=\frac{48}{24}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+24}{2*12}=\frac{96}{24}
=4
$