4/3x-2(9-1/3x)=-7/3x+9

Solution for 4/3x-2(9-1/3x)=-7/3x+9 equation:

4/3x-2(9-1/3x)=-7/3x+9

We move all terms to the left:

4/3x-2(9-1/3x)-(-7/3x+9)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

4/3x-2(-1/3x+9)-(-7/3x+9)=0

We multiply parentheses

4/3x+2x-(-7/3x+9)-18=0

We get rid of parentheses

4/3x+2x+7/3x-9-18=0

We multiply all the terms by the denominator


2x*3x-9*3x-18*3x+4+7=0

We add all the numbers together, and all the variables

2x*3x-9*3x-18*3x+11=0

Wy multiply elements

6x^2-27x-54x+11=0

We add all the numbers together, and all the variables

6x^2-81x+11=0

a = 6; b = -81; c = +11;
Δ = b2-4ac
Δ = -812-4·6·11
Δ = 6297
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{-(-81)-\sqrt{6297}}{2*6}=\frac{81-\sqrt{6297}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+\sqrt{6297}}{2*6}=\frac{81+\sqrt{6297}}{12}
$