1/3x+120=x

Solution for 1/3x+120=x equation:

1/3x+120=x

We move all terms to the left:

1/3x+120-(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+120=0

We multiply all the terms by the denominator


-1x*3x+120*3x+1=0

Wy multiply elements

-3x^2+360x+1=0

a = -3; b = 360; c = +1;
Δ = b2-4ac
Δ = 3602-4·(-3)·1
Δ = 129612
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:

$\sqrt{\Delta}=\sqrt{129612}=\sqrt{4*32403}=\sqrt{4}*\sqrt{32403}=2\sqrt{32403}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-2\sqrt{32403}}{2*-3}=\frac{-360-2\sqrt{32403}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+2\sqrt{32403}}{2*-3}=\frac{-360+2\sqrt{32403}}{-6}
$