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

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

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

We move all terms to the left:

3/x+1-1/2-(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

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

We calculate fractions


(-9x^2)/12x^2+36x/12x^2+(-8x)/12x^2+1+1=0

We add all the numbers together, and all the variables

(-9x^2)/12x^2+36x/12x^2+(-8x)/12x^2+2=0

We multiply all the terms by the denominator


(-9x^2)+36x+(-8x)+2*12x^2=0

Wy multiply elements

(-9x^2)+24x^2+36x+(-8x)=0

We get rid of parentheses

-9x^2+24x^2+36x-8x=0

We add all the numbers together, and all the variables

15x^2+28x=0

a = 15; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·15·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*15}=\frac{-56}{30}
=-1+13/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*15}=\frac{0}{30}
=0
$