(3x-6/12x-24)(x+3)=0

Solution for (3x-6/12x-24)(x+3)=0 equation:

(3x-6/12x-24)(x+3)=0


Domain of the equation: 12x-24)(x+3)!=0

x∈R


We multiply parentheses ..

(+3x^2+9x-6x^2-18x-24x-72)=0

We get rid of parentheses

3x^2-6x^2+9x-18x-24x-72=0

We add all the numbers together, and all the variables

-3x^2-33x-72=0

a = -3; b = -33; c = -72;
Δ = b2-4ac
Δ = -332-4·(-3)·(-72)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-15}{2*-3}=\frac{18}{-6}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+15}{2*-3}=\frac{48}{-6}
=-8
$