3/2x=6/x-3

Solution for 3/2x=6/x-3 equation:

3/2x=6/x-3

We move all terms to the left:

3/2x-(6/x-3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

3/2x-6/x+3=0

We calculate fractions


3x/2x^2+(-12x)/2x^2+3=0

We multiply all the terms by the denominator


3x+(-12x)+3*2x^2=0

Wy multiply elements

6x^2+3x+(-12x)=0

We get rid of parentheses

6x^2+3x-12x=0

We add all the numbers together, and all the variables

6x^2-9x=0

a = 6; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·6·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*6}=\frac{18}{12}
=1+1/2
$