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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-9x^2)/12x^2+12x/12x^2+(-8x)/12x^2+1=0

We multiply all the terms by the denominator


(-9x^2)+12x+(-8x)+1*12x^2=0

Wy multiply elements

(-9x^2)+12x^2+12x+(-8x)=0

We get rid of parentheses

-9x^2+12x^2+12x-8x=0

We add all the numbers together, and all the variables

3x^2+4x=0

a = 3; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·3·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*3}=\frac{-8}{6}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*3}=\frac{0}{6}
=0
$