3x+9=9/3x-11+2

Solution for 3x+9=9/3x-11+2 equation:

3x+9=9/3x-11+2

We move all terms to the left:

3x+9-(9/3x-11+2)=0


Domain of the equation: 3x-11+2)!=0

We move all terms containing x to the left, all other terms to the right

3x+2)!=11

x∈R


We add all the numbers together, and all the variables

3x-(9/3x-9)+9=0

We get rid of parentheses

3x-9/3x+9+9=0

We multiply all the terms by the denominator


3x*3x+9*3x+9*3x-9=0

Wy multiply elements

9x^2+27x+27x-9=0

We add all the numbers together, and all the variables

9x^2+54x-9=0

a = 9; b = 54; c = -9;
Δ = b2-4ac
Δ = 542-4·9·(-9)
Δ = 3240
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:

$\sqrt{\Delta}=\sqrt{3240}=\sqrt{324*10}=\sqrt{324}*\sqrt{10}=18\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-18\sqrt{10}}{2*9}=\frac{-54-18\sqrt{10}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+18\sqrt{10}}{2*9}=\frac{-54+18\sqrt{10}}{18}
$