x=540-1/3x

Solution for x=540-1/3x equation:

x=540-1/3x

We move all terms to the left:

x-(540-1/3x)=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-(-1/3x+540)=0

We get rid of parentheses

x+1/3x-540=0

We multiply all the terms by the denominator


x*3x-540*3x+1=0

Wy multiply elements

3x^2-1620x+1=0

a = 3; b = -1620; c = +1;
Δ = b2-4ac
Δ = -16202-4·3·1
Δ = 2624388
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:

$\sqrt{\Delta}=\sqrt{2624388}=\sqrt{4*656097}=\sqrt{4}*\sqrt{656097}=2\sqrt{656097}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1620)-2\sqrt{656097}}{2*3}=\frac{1620-2\sqrt{656097}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1620)+2\sqrt{656097}}{2*3}=\frac{1620+2\sqrt{656097}}{6}
$