(6x-3)(4x-12)=0

Solution for (6x-3)(4x-12)=0 equation:

(6x-3)(4x-12)=0

We multiply parentheses ..

(+24x^2-72x-12x+36)=0

We get rid of parentheses

24x^2-72x-12x+36=0

We add all the numbers together, and all the variables

24x^2-84x+36=0

a = 24; b = -84; c = +36;
Δ = b2-4ac
Δ = -842-4·24·36
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-60}{2*24}=\frac{24}{48}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+60}{2*24}=\frac{144}{48}
=3
$