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-3=0

Wy multiply elements

6x^2-27x-54x-3=0

We add all the numbers together, and all the variables

6x^2-81x-3=0

a = 6; b = -81; c = -3;
Δ = b2-4ac
Δ = -812-4·6·(-3)
Δ = 6633
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:

$\sqrt{\Delta}=\sqrt{6633}=\sqrt{9*737}=\sqrt{9}*\sqrt{737}=3\sqrt{737}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-3\sqrt{737}}{2*6}=\frac{81-3\sqrt{737}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+3\sqrt{737}}{2*6}=\frac{81+3\sqrt{737}}{12}
$