x+(2/3x)=120

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

x+(2/3x)=120

We move all terms to the left:

x+(2/3x)-(120)=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}
$