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

Solution for -4x^2/(4x+8)+2x/(4x+8)=0 equation:

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


Domain of the equation: (4x+8)!=0

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

4x!=-8

x!=-8/4

x!=-2

x∈R


We multiply all the terms by the denominator


-4x^2+2x=0

a = -4; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-4)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-4}=\frac{-4}{-8}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-4}=\frac{0}{-8}
=0
$