2+1x=2+2/3x

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

2+1x=2+2/3x

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

3x^2-2=0

a = 3; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·3·(-2)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*3}=\frac{0-2\sqrt{6}}{6}
=-\frac{2\sqrt{6}}{6}
=-\frac{\sqrt{6}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*3}=\frac{0+2\sqrt{6}}{6}
=\frac{2\sqrt{6}}{6}
=\frac{\sqrt{6}}{3}
$