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

Wy multiply elements

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

We get rid of parentheses

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