2x+9/3=2/3x

Solution for 2x+9/3=2/3x equation:

2x+9/3=2/3x

We move all terms to the left:

2x+9/3-(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

2x-(+2/3x)+9/3=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

2x-2/3x+3=0

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2+9x-2=0

a = 6; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·6·(-2)
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{-(9)-\sqrt{129}}{2*6}=\frac{-9-\sqrt{129}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{129}}{2*6}=\frac{-9+\sqrt{129}}{12}
$