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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((+2x^2+12x-4x-24))=0


We calculate terms in parentheses: -((+2x^2+12x-4x-24)), so:

(+2x^2+12x-4x-24)

We get rid of parentheses

2x^2+12x-4x-24

We add all the numbers together, and all the variables

2x^2+8x-24

Back to the equation:

-(2x^2+8x-24)


We get rid of parentheses

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

a = -2; b = -8; c = +24;
Δ = b2-4ac
Δ = -82-4·(-2)·24
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16}{2*-2}=\frac{-8}{-4}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16}{2*-2}=\frac{24}{-4}
=-6
$