9+1/3x=7/3x+9-2x

Solution for 9+1/3x=7/3x+9-2x equation:

9+1/3x=7/3x+9-2x

We move all terms to the left:

9+1/3x-(7/3x+9-2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3x+9-2x)!=0

We move all terms containing x to the left, all other terms to the right

3x-2x)!=-9

x∈R


We add all the numbers together, and all the variables

1/3x-(-2x+7/3x+9)+9=0

We get rid of parentheses

1/3x+2x-7/3x-9+9=0

We multiply all the terms by the denominator


2x*3x-9*3x+9*3x+1-7=0

We add all the numbers together, and all the variables

2x*3x-9*3x+9*3x-6=0

Wy multiply elements

6x^2-27x+27x-6=0

We add all the numbers together, and all the variables

6x^2-6=0

a = 6; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·6·(-6)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*6}=\frac{12}{12}
=1
$