12(x-8)(3x+1)=0

Solution for 12(x-8)(3x+1)=0 equation:

12(x-8)(3x+1)=0

We multiply parentheses ..

12(+3x^2+x-24x-8)=0

We multiply parentheses

36x^2+12x-288x-96=0

We add all the numbers together, and all the variables

36x^2-276x-96=0

a = 36; b = -276; c = -96;
Δ = b2-4ac
Δ = -2762-4·36·(-96)
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-276)-300}{2*36}=\frac{-24}{72}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-276)+300}{2*36}=\frac{576}{72}
=8
$