3/2x=5/x-2

Solution for 3/2x=5/x-2 equation:

3/2x=5/x-2

We move all terms to the left:

3/2x-(5/x-2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x-2)!=0

x∈R


We get rid of parentheses

3/2x-5/x+2=0

We calculate fractions


3x/2x^2+(-10x)/2x^2+2=0

We multiply all the terms by the denominator


3x+(-10x)+2*2x^2=0

Wy multiply elements

4x^2+3x+(-10x)=0

We get rid of parentheses

4x^2+3x-10x=0

We add all the numbers together, and all the variables

4x^2-7x=0

a = 4; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·4·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*4}=\frac{14}{8}
=1+3/4
$