2/3x+1/3x=6+x-2/3x

Solution for 2/3x+1/3x=6+x-2/3x equation:

2/3x+1/3x=6+x-2/3x

We move all terms to the left:

2/3x+1/3x-(6+x-2/3x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x+1/3x-(x-2/3x+6)=0

We get rid of parentheses

2/3x+1/3x-x+2/3x-6=0

We multiply all the terms by the denominator


-x*3x-6*3x+2+1+2=0

We add all the numbers together, and all the variables

-x*3x-6*3x+5=0

Wy multiply elements

-3x^2-18x+5=0

a = -3; b = -18; c = +5;
Δ = b2-4ac
Δ = -182-4·(-3)·5
Δ = 384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-8\sqrt{6}}{2*-3}=\frac{18-8\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+8\sqrt{6}}{2*-3}=\frac{18+8\sqrt{6}}{-6}
$