(2/3)x+(1/3)=x+2

Solution for (2/3)x+(1/3)=x+2 equation:

(2/3)x+(1/3)=x+2

We move all terms to the left:

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


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x^2*3-x*3-5=0

Wy multiply elements

6x^2-3x-5=0

a = 6; b = -3; c = -5;
Δ = b2-4ac
Δ = -32-4·6·(-5)
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{129}}{2*6}=\frac{3-\sqrt{129}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{129}}{2*6}=\frac{3+\sqrt{129}}{12}
$