H(x)=x(-2x-4)

Solution for H(x)=x(-2x-4) equation:

(H)=H(-2H-4)

We move all terms to the left:

(H)-(H(-2H-4))=0


We calculate terms in parentheses: -(H(-2H-4)), so:

H(-2H-4)

We multiply parentheses

-2H^2-4H

Back to the equation:

-(-2H^2-4H)


We get rid of parentheses

2H^2+4H+H=0

We add all the numbers together, and all the variables

2H^2+5H=0

a = 2; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·2·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*2}=\frac{-10}{4}
=-2+1/2
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*2}=\frac{0}{4}
=0
$