(3x+12)(4x-20)=0

Solution for (3x+12)(4x-20)=0 equation:

(3x+12)(4x-20)=0

We multiply parentheses ..

(+12x^2-60x+48x-240)=0

We get rid of parentheses

12x^2-60x+48x-240=0

We add all the numbers together, and all the variables

12x^2-12x-240=0

a = 12; b = -12; c = -240;
Δ = b2-4ac
Δ = -122-4·12·(-240)
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-108}{2*12}=\frac{-96}{24}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+108}{2*12}=\frac{120}{24}
=5
$