1/3*x+166=x

Solution for 1/3*x+166=x equation:

1/3x+166=x

We move all terms to the left:

1/3x+166-(x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/3x+166=0

We multiply all the terms by the denominator


-1x*3x+166*3x+1=0

Wy multiply elements

-3x^2+498x+1=0

a = -3; b = 498; c = +1;
Δ = b2-4ac
Δ = 4982-4·(-3)·1
Δ = 248016
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:

$\sqrt{\Delta}=\sqrt{248016}=\sqrt{16*15501}=\sqrt{16}*\sqrt{15501}=4\sqrt{15501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(498)-4\sqrt{15501}}{2*-3}=\frac{-498-4\sqrt{15501}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(498)+4\sqrt{15501}}{2*-3}=\frac{-498+4\sqrt{15501}}{-6}
$