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

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

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

We move all terms to the left:

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

We multiply parentheses

2x-(-4x(x+4))+16=0


We calculate terms in parentheses: -(-4x(x+4)), so:

-4x(x+4)

We multiply parentheses

-4x^2-16x

Back to the equation:

-(-4x^2-16x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2+18x+16=0

a = 4; b = 18; c = +16;
Δ = b2-4ac
Δ = 182-4·4·16
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{17}}{2*4}=\frac{-18-2\sqrt{17}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{17}}{2*4}=\frac{-18+2\sqrt{17}}{8}
$