2x+1/3x=518

Solution for 2x+1/3x=518 equation:

2x+1/3x=518

We move all terms to the left:

2x+1/3x-(518)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


2x*3x-518*3x+1=0

Wy multiply elements

6x^2-1554x+1=0

a = 6; b = -1554; c = +1;
Δ = b2-4ac
Δ = -15542-4·6·1
Δ = 2414892
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:

$\sqrt{\Delta}=\sqrt{2414892}=\sqrt{4*603723}=\sqrt{4}*\sqrt{603723}=2\sqrt{603723}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1554)-2\sqrt{603723}}{2*6}=\frac{1554-2\sqrt{603723}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1554)+2\sqrt{603723}}{2*6}=\frac{1554+2\sqrt{603723}}{12}
$