(x-36)+(1/3x)=180

Solution for (x-36)+(1/3x)=180 equation:

(x-36)+(1/3x)=180

We move all terms to the left:

(x-36)+(1/3x)-(180)=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-36)+(+1/3x)-180=0

We get rid of parentheses

x+1/3x-36-180=0

We multiply all the terms by the denominator


x*3x-36*3x-180*3x+1=0

Wy multiply elements

3x^2-108x-540x+1=0

We add all the numbers together, and all the variables

3x^2-648x+1=0

a = 3; b = -648; c = +1;
Δ = b2-4ac
Δ = -6482-4·3·1
Δ = 419892
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:

$\sqrt{\Delta}=\sqrt{419892}=\sqrt{4*104973}=\sqrt{4}*\sqrt{104973}=2\sqrt{104973}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-648)-2\sqrt{104973}}{2*3}=\frac{648-2\sqrt{104973}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-648)+2\sqrt{104973}}{2*3}=\frac{648+2\sqrt{104973}}{6}
$