(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+60x-36=0

a = 24; b = 60; c = -36;
Δ = b2-4ac
Δ = 602-4·24·(-36)
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-84}{2*24}=\frac{-144}{48}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+84}{2*24}=\frac{24}{48}
=1/2
$