4/2x+6=2/6x

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

4/2x+6=2/6x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


24x/12x^2+(-4x)/12x^2+6=0

We multiply all the terms by the denominator


24x+(-4x)+6*12x^2=0

Wy multiply elements

72x^2+24x+(-4x)=0

We get rid of parentheses

72x^2+24x-4x=0

We add all the numbers together, and all the variables

72x^2+20x=0

a = 72; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·72·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*72}=\frac{-40}{144}
=-5/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*72}=\frac{0}{144}
=0
$