x+1/3x+2/3x-4=39

Solution for x+1/3x+2/3x-4=39 equation:

x+1/3x+2/3x-4=39

We move all terms to the left:

x+1/3x+2/3x-4-(39)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/3x+2/3x-43=0

We multiply all the terms by the denominator


x*3x-43*3x+1+2=0

We add all the numbers together, and all the variables

x*3x-43*3x+3=0

Wy multiply elements

3x^2-129x+3=0

a = 3; b = -129; c = +3;
Δ = b2-4ac
Δ = -1292-4·3·3
Δ = 16605
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{16605}=\sqrt{81*205}=\sqrt{81}*\sqrt{205}=9\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-129)-9\sqrt{205}}{2*3}=\frac{129-9\sqrt{205}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-129)+9\sqrt{205}}{2*3}=\frac{129+9\sqrt{205}}{6}
$