2x+1/3x+1x=117

Solution for 2x+1/3x+1x=117 equation:

2x+1/3x+1x=117

We move all terms to the left:

2x+1/3x+1x-(117)=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+1/3x-117=0

We multiply all the terms by the denominator


3x*3x-117*3x+1=0

Wy multiply elements

9x^2-351x+1=0

a = 9; b = -351; c = +1;
Δ = b2-4ac
Δ = -3512-4·9·1
Δ = 123165
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:

$\sqrt{\Delta}=\sqrt{123165}=\sqrt{9*13685}=\sqrt{9}*\sqrt{13685}=3\sqrt{13685}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-351)-3\sqrt{13685}}{2*9}=\frac{351-3\sqrt{13685}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-351)+3\sqrt{13685}}{2*9}=\frac{351+3\sqrt{13685}}{18}
$