(2x-4)(6+9x)=0

Solution for (2x-4)(6+9x)=0 equation:

(2x-4)(6+9x)=0

We add all the numbers together, and all the variables

(2x-4)(9x+6)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

18x^2-24x-24=0

a = 18; b = -24; c = -24;
Δ = b2-4ac
Δ = -242-4·18·(-24)
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*18}=\frac{-24}{36}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+48}{2*18}=\frac{72}{36}
=2
$