2/3x+4=6-2/6x

Solution for 2/3x+4=6-2/6x equation:

2/3x+4=6-2/6x

We move all terms to the left:

2/3x+4-(6-2/6x)=0


Domain of the equation: 3x!=0

x!=0/3

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

2/3x-(-2/6x+6)+4=0

We get rid of parentheses

2/3x+2/6x-6+4=0

We calculate fractions


12x/18x^2+6x/18x^2-6+4=0

We add all the numbers together, and all the variables

12x/18x^2+6x/18x^2-2=0

We multiply all the terms by the denominator


12x+6x-2*18x^2=0

We add all the numbers together, and all the variables

18x-2*18x^2=0

Wy multiply elements

-36x^2+18x=0

a = -36; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-36)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-36}=\frac{-36}{-72}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-36}=\frac{0}{-72}
=0
$