(4x-9)(6x+12)=0

Solution for (4x-9)(6x+12)=0 equation:

(4x-9)(6x+12)=0

We multiply parentheses ..

(+24x^2+48x-54x-108)=0

We get rid of parentheses

24x^2+48x-54x-108=0

We add all the numbers together, and all the variables

24x^2-6x-108=0

a = 24; b = -6; c = -108;
Δ = b2-4ac
Δ = -62-4·24·(-108)
Δ = 10404
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10404}=102$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-102}{2*24}=\frac{-96}{48}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+102}{2*24}=\frac{108}{48}
=2+1/4
$