2x+1/3x=221

Solution for 2x+1/3x=221 equation:

2x+1/3x=221

We move all terms to the left:

2x+1/3x-(221)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


2x*3x-221*3x+1=0

Wy multiply elements

6x^2-663x+1=0

a = 6; b = -663; c = +1;
Δ = b2-4ac
Δ = -6632-4·6·1
Δ = 439545
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{-(-663)-\sqrt{439545}}{2*6}=\frac{663-\sqrt{439545}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-663)+\sqrt{439545}}{2*6}=\frac{663+\sqrt{439545}}{12}
$