0=3x-1/x+1

Solution for 0=3x-1/x+1 equation:

0=3x-1/x+1

We move all terms to the left:

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


Domain of the equation: x+1)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-3x+1/x-1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -3; b = -1; c = +1;
Δ = b2-4ac
Δ = -12-4·(-3)·1
Δ = 13
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{-(-1)-\sqrt{13}}{2*-3}=\frac{1-\sqrt{13}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{13}}{2*-3}=\frac{1+\sqrt{13}}{-6}
$