1/x=(2)/3x-1

Solution for 1/x=(2)/3x-1 equation:

1/x=(2)/3x-1

We move all terms to the left:

1/x-((2)/3x-1)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


3x/3x^2+(-2x)/3x^2+1=0

We multiply all the terms by the denominator


3x+(-2x)+1*3x^2=0

Wy multiply elements

3x^2+3x+(-2x)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2+x=0

a = 3; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·3·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*3}=\frac{-2}{6}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*3}=\frac{0}{6}
=0
$