X+1/3x=165

Solution for X+1/3x=165 equation:

X+1/3X=165

We move all terms to the left:

X+1/3X-(165)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-165*3X+1=0

Wy multiply elements

3X^2-495X+1=0

a = 3; b = -495; c = +1;
Δ = b2-4ac
Δ = -4952-4·3·1
Δ = 245013
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{-(-495)-\sqrt{245013}}{2*3}=\frac{495-\sqrt{245013}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-495)+\sqrt{245013}}{2*3}=\frac{495+\sqrt{245013}}{6}
$