(2x-8)(3x+6)=0

Solution for (2x-8)(3x+6)=0 equation:

(2x-8)(3x+6)=0

We multiply parentheses ..

(+6x^2+12x-24x-48)=0

We get rid of parentheses

6x^2+12x-24x-48=0

We add all the numbers together, and all the variables

6x^2-12x-48=0

a = 6; b = -12; c = -48;
Δ = b2-4ac
Δ = -122-4·6·(-48)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-36}{2*6}=\frac{-24}{12}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+36}{2*6}=\frac{48}{12}
=4
$