(3x-12)(4x-2)=0

Solution for (3x-12)(4x-2)=0 equation:

(3x-12)(4x-2)=0

We multiply parentheses ..

(+12x^2-6x-48x+24)=0

We get rid of parentheses

12x^2-6x-48x+24=0

We add all the numbers together, and all the variables

12x^2-54x+24=0

a = 12; b = -54; c = +24;
Δ = b2-4ac
Δ = -542-4·12·24
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-42}{2*12}=\frac{12}{24}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+42}{2*12}=\frac{96}{24}
=4
$