1/3x+x=208

Solution for 1/3x+x=208 equation:

1/3x+x=208

We move all terms to the left:

1/3x+x-(208)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/3x-208=0

We multiply all the terms by the denominator


x*3x-208*3x+1=0

Wy multiply elements

3x^2-624x+1=0

a = 3; b = -624; c = +1;
Δ = b2-4ac
Δ = -6242-4·3·1
Δ = 389364
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:

$\sqrt{\Delta}=\sqrt{389364}=\sqrt{4*97341}=\sqrt{4}*\sqrt{97341}=2\sqrt{97341}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-624)-2\sqrt{97341}}{2*3}=\frac{624-2\sqrt{97341}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-624)+2\sqrt{97341}}{2*3}=\frac{624+2\sqrt{97341}}{6}
$