x+2/2=2/3x

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

x+2/2=2/3x

We move all terms to the left:

x+2/2-(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

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

x-2/3x+1=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2+3x-2=0

a = 3; b = 3; c = -2;
Δ = b2-4ac
Δ = 32-4·3·(-2)
Δ = 33
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{33}}{2*3}=\frac{-3-\sqrt{33}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{33}}{2*3}=\frac{-3+\sqrt{33}}{6}
$