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

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

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

We multiply parentheses ..

12(+s^2-4s+8s-32)=0

We multiply parentheses

12s^2-48s+96s-384=0

We add all the numbers together, and all the variables

12s^2+48s-384=0

a = 12; b = 48; c = -384;
Δ = b2-4ac
Δ = 482-4·12·(-384)
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-144}{2*12}=\frac{-192}{24}
=-8
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+144}{2*12}=\frac{96}{24}
=4
$