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)=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


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

6x^2-54x+11=0

a = 6; b = -54; c = +11;
Δ = b2-4ac
Δ = -542-4·6·11
Δ = 2652
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:

$\sqrt{\Delta}=\sqrt{2652}=\sqrt{4*663}=\sqrt{4}*\sqrt{663}=2\sqrt{663}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{663}}{2*6}=\frac{54-2\sqrt{663}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{663}}{2*6}=\frac{54+2\sqrt{663}}{12}
$