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

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

(X+12)(X-4)=0

We multiply parentheses ..

(+X^2-4X+12X-48)=0

We get rid of parentheses

X^2-4X+12X-48=0

We add all the numbers together, and all the variables

X^2+8X-48=0

a = 1; b = 8; c = -48;
Δ = b2-4ac
Δ = 82-4·1·(-48)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16}{2*1}=\frac{-24}{2}
=-12
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16}{2*1}=\frac{8}{2}
=4
$