2(x+1)=2/3x=9

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

2(x+1)=2/3x=9

We move all terms to the left:

2(x+1)-(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

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

We multiply parentheses

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

We get rid of parentheses

2x-2/3x+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2+6x-2=0

a = 6; b = 6; c = -2;
Δ = b2-4ac
Δ = 62-4·6·(-2)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{21}}{2*6}=\frac{-6-2\sqrt{21}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{21}}{2*6}=\frac{-6+2\sqrt{21}}{12}
$