(3x-6)(4x+6)=0

Solution for (3x-6)(4x+6)=0 equation:

(3x-6)(4x+6)=0

We multiply parentheses ..

(+12x^2+18x-24x-36)=0

We get rid of parentheses

12x^2+18x-24x-36=0

We add all the numbers together, and all the variables

12x^2-6x-36=0

a = 12; b = -6; c = -36;
Δ = b2-4ac
Δ = -62-4·12·(-36)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-42}{2*12}=\frac{-36}{24}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+42}{2*12}=\frac{48}{24}
=2
$