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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2-6x+2=0

a = 3; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·3·2
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{3}}{2*3}=\frac{6-2\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{3}}{2*3}=\frac{6+2\sqrt{3}}{6}
$