x+2/3x+2x-15=106

Solution for x+2/3x+2x-15=106 equation:

x+2/3x+2x-15=106

We move all terms to the left:

x+2/3x+2x-15-(106)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3x+2/3x-121=0

We multiply all the terms by the denominator


3x*3x-121*3x+2=0

Wy multiply elements

9x^2-363x+2=0

a = 9; b = -363; c = +2;
Δ = b2-4ac
Δ = -3632-4·9·2
Δ = 131697
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:

$\sqrt{\Delta}=\sqrt{131697}=\sqrt{9*14633}=\sqrt{9}*\sqrt{14633}=3\sqrt{14633}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-363)-3\sqrt{14633}}{2*9}=\frac{363-3\sqrt{14633}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-363)+3\sqrt{14633}}{2*9}=\frac{363+3\sqrt{14633}}{18}
$