3x+11=2/3x

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

3x+11=2/3x

We move all terms to the left:

3x+11-(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

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

We get rid of parentheses

3x-2/3x+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}
$