3/z+9=-3/5z

Solution for 3/z+9=-3/5z equation:

3/z+9=-3/5z

We move all terms to the left:

3/z+9-(-3/5z)=0


Domain of the equation: z!=0

z∈R



Domain of the equation: 5z)!=0

z!=0/1

z!=0

z∈R


We get rid of parentheses

3/z+3/5z+9=0

We calculate fractions


15z/5z^2+3z/5z^2+9=0

We multiply all the terms by the denominator


15z+3z+9*5z^2=0

We add all the numbers together, and all the variables

18z+9*5z^2=0

Wy multiply elements

45z^2+18z=0

a = 45; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·45·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*45}=\frac{-36}{90}
=-2/5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*45}=\frac{0}{90}
=0
$