-8/2x+2=-8/4x+6

Solution for -8/2x+2=-8/4x+6 equation:

-8/2x+2=-8/4x+6

We move all terms to the left:

-8/2x+2-(-8/4x+6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+6)!=0

x∈R


We get rid of parentheses

-8/2x+8/4x-6+2=0

We calculate fractions


(-32x)/8x^2+16x/8x^2-6+2=0

We add all the numbers together, and all the variables

(-32x)/8x^2+16x/8x^2-4=0

We multiply all the terms by the denominator


(-32x)+16x-4*8x^2=0

We add all the numbers together, and all the variables

16x+(-32x)-4*8x^2=0

Wy multiply elements

-32x^2+16x+(-32x)=0

We get rid of parentheses

-32x^2+16x-32x=0

We add all the numbers together, and all the variables

-32x^2-16x=0

a = -32; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-32)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-32}=\frac{0}{-64}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-32}=\frac{32}{-64}
=-1/2
$