1/3x=180-x

Solution for 1/3x=180-x equation:

1/3x=180-x

We move all terms to the left:

1/3x-(180-x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(-1x+180)=0

We get rid of parentheses

1/3x+1x-180=0

We multiply all the terms by the denominator


1x*3x-180*3x+1=0

Wy multiply elements

3x^2-540x+1=0

a = 3; b = -540; c = +1;
Δ = b2-4ac
Δ = -5402-4·3·1
Δ = 291588
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:

$\sqrt{\Delta}=\sqrt{291588}=\sqrt{8836*33}=\sqrt{8836}*\sqrt{33}=94\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-94\sqrt{33}}{2*3}=\frac{540-94\sqrt{33}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+94\sqrt{33}}{2*3}=\frac{540+94\sqrt{33}}{6}
$