120=x+2/3x

Solution for 120=x+2/3x equation:

120=x+2/3x

We move all terms to the left:

120-(x+2/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x+2/3x)+120=0

We get rid of parentheses

-x-2/3x+120=0

We multiply all the terms by the denominator


-x*3x+120*3x-2=0

Wy multiply elements

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

a = -3; b = 360; c = -2;
Δ = b2-4ac
Δ = 3602-4·(-3)·(-2)
Δ = 129576
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:

$\sqrt{\Delta}=\sqrt{129576}=\sqrt{4*32394}=\sqrt{4}*\sqrt{32394}=2\sqrt{32394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-2\sqrt{32394}}{2*-3}=\frac{-360-2\sqrt{32394}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+2\sqrt{32394}}{2*-3}=\frac{-360+2\sqrt{32394}}{-6}
$