(x)+(1/3x-1)=139

Solution for (x)+(1/3x-1)=139 equation:

(x)+(1/3x-1)=139

We move all terms to the left:

(x)+(1/3x-1)-(139)=0


Domain of the equation: 3x-1)!=0

x∈R


We get rid of parentheses

x+1/3x-1-139=0

We multiply all the terms by the denominator


x*3x-1*3x-139*3x+1=0

Wy multiply elements

3x^2-3x-417x+1=0

We add all the numbers together, and all the variables

3x^2-420x+1=0

a = 3; b = -420; c = +1;
Δ = b2-4ac
Δ = -4202-4·3·1
Δ = 176388
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:

$\sqrt{\Delta}=\sqrt{176388}=\sqrt{4*44097}=\sqrt{4}*\sqrt{44097}=2\sqrt{44097}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-2\sqrt{44097}}{2*3}=\frac{420-2\sqrt{44097}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+2\sqrt{44097}}{2*3}=\frac{420+2\sqrt{44097}}{6}
$