2x+1/3x=6

Solution for 2x+1/3x=6 equation:

2x+1/3x=6

We move all terms to the left:

2x+1/3x-(6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


2x*3x-6*3x+1=0

Wy multiply elements

6x^2-18x+1=0

a = 6; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·6·1
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-10\sqrt{3}}{2*6}=\frac{18-10\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+10\sqrt{3}}{2*6}=\frac{18+10\sqrt{3}}{12}
$