7/3x+2x=117

Solution for 7/3x+2x=117 equation:

7/3x+2x=117

We move all terms to the left:

7/3x+2x-(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

2x+7/3x-117=0

We multiply all the terms by the denominator


2x*3x-117*3x+7=0

Wy multiply elements

6x^2-351x+7=0

a = 6; b = -351; c = +7;
Δ = b2-4ac
Δ = -3512-4·6·7
Δ = 123033
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-351)-\sqrt{123033}}{2*6}=\frac{351-\sqrt{123033}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-351)+\sqrt{123033}}{2*6}=\frac{351+\sqrt{123033}}{12}
$