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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


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

2(-1x-8)2x

We multiply parentheses

-4x^2-32x

Back to the equation:

-(-4x^2-32x)


We get rid of parentheses

4x^2+32x+2x+8=0

We add all the numbers together, and all the variables

4x^2+34x+8=0

a = 4; b = 34; c = +8;
Δ = b2-4ac
Δ = 342-4·4·8
Δ = 1028
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1028}=\sqrt{4*257}=\sqrt{4}*\sqrt{257}=2\sqrt{257}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{257}}{2*4}=\frac{-34-2\sqrt{257}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{257}}{2*4}=\frac{-34+2\sqrt{257}}{8}
$