0=0.5(x-2)(x+4)

Solution for 0=0.5(x-2)(x+4) equation:

0=0.5(x-2)(x+4)

We move all terms to the left:

0-(0.5(x-2)(x+4))=0

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-(0.5(+x^2+4x-2x-8))=0


We calculate terms in parentheses: -(0.5(+x^2+4x-2x-8)), so:

0.5(+x^2+4x-2x-8)

We multiply parentheses

0.5x^2+2x-1x-4

We add all the numbers together, and all the variables

0.5x^2+x-4

Back to the equation:

-(0.5x^2+x-4)


We get rid of parentheses

-0.5x^2-x+4=0

We add all the numbers together, and all the variables

-0.5x^2-1x+4=0

a = -0.5; b = -1; c = +4;
Δ = b2-4ac
Δ = -12-4·(-0.5)·4
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3}{2*-0.5}=\frac{-2}{-1}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3}{2*-0.5}=\frac{4}{-1}
=-4
$