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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-9x^2)/12x^2+36x/12x^2+(-4x)/12x^2-3+1=0

We add all the numbers together, and all the variables

(-9x^2)/12x^2+36x/12x^2+(-4x)/12x^2-2=0

We multiply all the terms by the denominator


(-9x^2)+36x+(-4x)-2*12x^2=0

Wy multiply elements

(-9x^2)-24x^2+36x+(-4x)=0

We get rid of parentheses

-9x^2-24x^2+36x-4x=0

We add all the numbers together, and all the variables

-33x^2+32x=0

a = -33; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-33)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-33}=\frac{-64}{-66}
=32/33
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-33}=\frac{0}{-66}
=0
$