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

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

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

We move all terms to the left:

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

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

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

9x^2-1=0

a = 9; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·9·(-1)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*9}=\frac{-6}{18}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*9}=\frac{6}{18}
=1/3
$