x+1/3x+x-6=71

Solution for x+1/3x+x-6=71 equation:

x+1/3x+x-6=71

We move all terms to the left:

x+1/3x+x-6-(71)=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-77=0

We multiply all the terms by the denominator


2x*3x-77*3x+1=0

Wy multiply elements

6x^2-231x+1=0

a = 6; b = -231; c = +1;
Δ = b2-4ac
Δ = -2312-4·6·1
Δ = 53337
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{-(-231)-\sqrt{53337}}{2*6}=\frac{231-\sqrt{53337}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-231)+\sqrt{53337}}{2*6}=\frac{231+\sqrt{53337}}{12}
$