(4x-12)(x+9)=0

Solution for (4x-12)(x+9)=0 equation:

(4x-12)(x+9)=0

We multiply parentheses ..

(+4x^2+36x-12x-108)=0

We get rid of parentheses

4x^2+36x-12x-108=0

We add all the numbers together, and all the variables

4x^2+24x-108=0

a = 4; b = 24; c = -108;
Δ = b2-4ac
Δ = 242-4·4·(-108)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-48}{2*4}=\frac{-72}{8}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+48}{2*4}=\frac{24}{8}
=3
$