x+2/3x+x+2/3x=260

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Solution for x+2/3x+x+2/3x=260 equation: 



x+2/3x+x+2/3x=260

We move all terms to the left:

x+2/3x+x+2/3x-(260)=0



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



We add all the numbers together, and all the variables

2x+2/3x+2/3x-260=0

We multiply all the terms by the denominator


2x*3x-260*3x+2+2=0

We add all the numbers together, and all the variables

2x*3x-260*3x+4=0

Wy multiply elements

6x^2-780x+4=0

a = 6; b = -780; c = +4;
Δ = b2-4ac
Δ = -7802-4·6·4
Δ = 608304
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:


$\sqrt{\Delta}=\sqrt{608304}=\sqrt{16*38019}=\sqrt{16}*\sqrt{38019}=4\sqrt{38019}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-780)-4\sqrt{38019}}{2*6}=\frac{780-4\sqrt{38019}}{12}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-780)+4\sqrt{38019}}{2*6}=\frac{780+4\sqrt{38019}}{12}
$

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