1/3x+x-65+x=180

Solution for 1/3x+x-65+x=180 equation:

1/3x+x-65+x=180

We move all terms to the left:

1/3x+x-65+x-(180)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/3x-245=0

We multiply all the terms by the denominator


2x*3x-245*3x+1=0

Wy multiply elements

6x^2-735x+1=0

a = 6; b = -735; c = +1;
Δ = b2-4ac
Δ = -7352-4·6·1
Δ = 540201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-735)-\sqrt{540201}}{2*6}=\frac{735-\sqrt{540201}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-735)+\sqrt{540201}}{2*6}=\frac{735+\sqrt{540201}}{12}
$