4/2x=3/x-3

Solution for 4/2x=3/x-3 equation:

4/2x=3/x-3

We move all terms to the left:

4/2x-(3/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

4/2x-3/x+3=0

We calculate fractions


4x/2x^2+(-6x)/2x^2+3=0

We multiply all the terms by the denominator


4x+(-6x)+3*2x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2-2x=0

a = 6; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·6·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*6}=\frac{4}{12}
=1/3
$