(x-9)(2x+12)=0

Solution for (x-9)(2x+12)=0 equation:

(x-9)(2x+12)=0

We multiply parentheses ..

(+2x^2+12x-18x-108)=0

We get rid of parentheses

2x^2+12x-18x-108=0

We add all the numbers together, and all the variables

2x^2-6x-108=0

a = 2; b = -6; c = -108;
Δ = b2-4ac
Δ = -62-4·2·(-108)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-30}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+30}{2*2}=\frac{36}{4}
=9
$