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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


x*3x+x*3x-65*3x-180*3x+1=0

Wy multiply elements

3x^2+3x^2-195x-540x+1=0

We add all the numbers together, and all the variables

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}
$