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

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

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

We multiply parentheses ..

(+4x^2+32x-12x-96)=0

We get rid of parentheses

4x^2+32x-12x-96=0

We add all the numbers together, and all the variables

4x^2+20x-96=0

a = 4; b = 20; c = -96;
Δ = b2-4ac
Δ = 202-4·4·(-96)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-44}{2*4}=\frac{-64}{8}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+44}{2*4}=\frac{24}{8}
=3
$