(3x-24)(2x+6)=0

Solution for (3x-24)(2x+6)=0 equation:

(3x-24)(2x+6)=0

We multiply parentheses ..

(+6x^2+18x-48x-144)=0

We get rid of parentheses

6x^2+18x-48x-144=0

We add all the numbers together, and all the variables

6x^2-30x-144=0

a = 6; b = -30; c = -144;
Δ = b2-4ac
Δ = -302-4·6·(-144)
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-66}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+66}{2*6}=\frac{96}{12}
=8
$