(3x-9)(4+2x)=0

Solution for (3x-9)(4+2x)=0 equation:

(3x-9)(4+2x)=0

We add all the numbers together, and all the variables

(3x-9)(2x+4)=0

We multiply parentheses ..

(+6x^2+12x-18x-36)=0

We get rid of parentheses

6x^2+12x-18x-36=0

We add all the numbers together, and all the variables

6x^2-6x-36=0

a = 6; b = -6; c = -36;
Δ = b2-4ac
Δ = -62-4·6·(-36)
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*6}=\frac{-24}{12}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+30}{2*6}=\frac{36}{12}
=3
$