2x-1/3x+1=14

Solution for 2x-1/3x+1=14 equation:

2x-1/3x+1=14

We move all terms to the left:

2x-1/3x+1-(14)=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-1/3x-13=0

We multiply all the terms by the denominator


2x*3x-13*3x-1=0

Wy multiply elements

6x^2-39x-1=0

a = 6; b = -39; c = -1;
Δ = b2-4ac
Δ = -392-4·6·(-1)
Δ = 1545
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{-(-39)-\sqrt{1545}}{2*6}=\frac{39-\sqrt{1545}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1545}}{2*6}=\frac{39+\sqrt{1545}}{12}
$