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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-96x^2)/768x^2+256x/768x^2+(-2304x)/768x^2=0

We multiply all the terms by the denominator


(-96x^2)+256x+(-2304x)=0

We get rid of parentheses

-96x^2+256x-2304x=0

We add all the numbers together, and all the variables

-96x^2-2048x=0

a = -96; b = -2048; c = 0;
Δ = b2-4ac
Δ = -20482-4·(-96)·0
Δ = 4194304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4194304}=2048$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2048)-2048}{2*-96}=\frac{0}{-192}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2048)+2048}{2*-96}=\frac{4096}{-192}
=-21+1/3
$