1/2x-3=2/x

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

1/2x-3=2/x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


x/2x^2+(-4x)/2x^2-3=0

We multiply all the terms by the denominator


x+(-4x)-3*2x^2=0

Wy multiply elements

-6x^2+x+(-4x)=0

We get rid of parentheses

-6x^2+x-4x=0

We add all the numbers together, and all the variables

-6x^2-3x=0

a = -6; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-6)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-6}=\frac{6}{-12}
=-1/2
$