3/z+4=-3/5z

Solution for 3/z+4=-3/5z equation:

3/z+4=-3/5z

We move all terms to the left:

3/z+4-(-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+4=0

We calculate fractions


15z/5z^2+3z/5z^2+4=0

We multiply all the terms by the denominator


15z+3z+4*5z^2=0

We add all the numbers together, and all the variables

18z+4*5z^2=0

Wy multiply elements

20z^2+18z=0

a = 20; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·20·0
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*20}=\frac{-36}{40}
=-9/10
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*20}=\frac{0}{40}
=0
$