180=x+2/3x

Solution for 180=x+2/3x equation:

180=x+2/3x

We move all terms to the left:

180-(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)+180=0

We get rid of parentheses

-x-2/3x+180=0

We multiply all the terms by the denominator


-x*3x+180*3x-2=0

Wy multiply elements

-3x^2+540x-2=0

a = -3; b = 540; c = -2;
Δ = b2-4ac
Δ = 5402-4·(-3)·(-2)
Δ = 291576
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:

$\sqrt{\Delta}=\sqrt{291576}=\sqrt{4*72894}=\sqrt{4}*\sqrt{72894}=2\sqrt{72894}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(540)-2\sqrt{72894}}{2*-3}=\frac{-540-2\sqrt{72894}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(540)+2\sqrt{72894}}{2*-3}=\frac{-540+2\sqrt{72894}}{-6}
$