260=x+2/3x

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

260=x+2/3x

We move all terms to the left:

260-(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)+260=0

We get rid of parentheses

-x-2/3x+260=0

We multiply all the terms by the denominator


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

Wy multiply elements

-3x^2+780x-2=0

a = -3; b = 780; c = -2;
Δ = b2-4ac
Δ = 7802-4·(-3)·(-2)
Δ = 608376
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:

$\sqrt{\Delta}=\sqrt{608376}=\sqrt{4*152094}=\sqrt{4}*\sqrt{152094}=2\sqrt{152094}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(780)-2\sqrt{152094}}{2*-3}=\frac{-780-2\sqrt{152094}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(780)+2\sqrt{152094}}{2*-3}=\frac{-780+2\sqrt{152094}}{-6}
$