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

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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 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}
$

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