(4x+24)(2x-6)=0

Solution for (4x+24)(2x-6)=0 equation:

(4x+24)(2x-6)=0

We multiply parentheses ..

(+8x^2-24x+48x-144)=0

We get rid of parentheses

8x^2-24x+48x-144=0

We add all the numbers together, and all the variables

8x^2+24x-144=0

a = 8; b = 24; c = -144;
Δ = b2-4ac
Δ = 242-4·8·(-144)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-72}{2*8}=\frac{-96}{16}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+72}{2*8}=\frac{48}{16}
=3
$