3/2z=5/z+3

Solution for 3/2z=5/z+3 equation:

3/2z=5/z+3

We move all terms to the left:

3/2z-(5/z+3)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R



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

z∈R


We get rid of parentheses

3/2z-5/z-3=0

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-6z^2+3z+(-10z)=0

We get rid of parentheses

-6z^2+3z-10z=0

We add all the numbers together, and all the variables

-6z^2-7z=0

a = -6; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-6)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-6}=\frac{0}{-12}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-6}=\frac{14}{-12}
=-1+1/6
$