(3x+6)(x-4)=9

Solution for (3x+6)(x-4)=9 equation:

(3x+6)(x-4)=9

We move all terms to the left:

(3x+6)(x-4)-(9)=0

We multiply parentheses ..

(+3x^2-12x+6x-24)-9=0

We get rid of parentheses

3x^2-12x+6x-24-9=0

We add all the numbers together, and all the variables

3x^2-6x-33=0

a = 3; b = -6; c = -33;
Δ = b2-4ac
Δ = -62-4·3·(-33)
Δ = 432
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12\sqrt{3}}{2*3}=\frac{6-12\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12\sqrt{3}}{2*3}=\frac{6+12\sqrt{3}}{6}
$