2/3x=11+3x

Solution for 2/3x=11+3x equation:

2/3x=11+3x

We move all terms to the left:

2/3x-(11+3x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(3x+11)=0

We get rid of parentheses

2/3x-3x-11=0

We multiply all the terms by the denominator


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

Wy multiply elements

-9x^2-33x+2=0

a = -9; b = -33; c = +2;
Δ = b2-4ac
Δ = -332-4·(-9)·2
Δ = 1161
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:

$\sqrt{\Delta}=\sqrt{1161}=\sqrt{9*129}=\sqrt{9}*\sqrt{129}=3\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3\sqrt{129}}{2*-9}=\frac{33-3\sqrt{129}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3\sqrt{129}}{2*-9}=\frac{33+3\sqrt{129}}{-18}
$