2x(x+4)=2(-8-x)-2x

Solution for 2x(x+4)=2(-8-x)-2x equation:

2x(x+4)=2(-8-x)-2x

We move all terms to the left:

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

We add all the numbers together, and all the variables

2x(x+4)-(2(-1x-8)-2x)=0

We multiply parentheses

2x^2+8x-(2(-1x-8)-2x)=0


We calculate terms in parentheses: -(2(-1x-8)-2x), so:

2(-1x-8)-2x

We add all the numbers together, and all the variables

-2x+2(-1x-8)

We multiply parentheses

-2x-2x-16

We add all the numbers together, and all the variables

-4x-16

Back to the equation:

-(-4x-16)


We get rid of parentheses

2x^2+8x+4x+16=0

We add all the numbers together, and all the variables

2x^2+12x+16=0

a = 2; b = 12; c = +16;
Δ = b2-4ac
Δ = 122-4·2·16
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4}{2*2}=\frac{-16}{4}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4}{2*2}=\frac{-8}{4}
=-2
$