12(x-6)(3x+7)=0

Solution for 12(x-6)(3x+7)=0 equation:

12(x-6)(3x+7)=0

We multiply parentheses ..

12(+3x^2+7x-18x-42)=0

We multiply parentheses

36x^2+84x-216x-504=0

We add all the numbers together, and all the variables

36x^2-132x-504=0

a = 36; b = -132; c = -504;
Δ = b2-4ac
Δ = -1322-4·36·(-504)
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{-(-132)-300}{2*36}=\frac{-168}{72}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+300}{2*36}=\frac{432}{72}
=6
$