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

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

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

We move all terms to the left:

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


Domain of the equation: (x+2)!=0

We move all terms containing x to the left, all other terms to the right

x!=-2

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -4; b = -4; c = +8;
Δ = b2-4ac
Δ = -42-4·(-4)·8
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-12}{2*-4}=\frac{-8}{-8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+12}{2*-4}=\frac{16}{-8}
=-2
$