z+5/z-5=9/z-5

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

z+5/z-5=9/z-5

We move all terms to the left:

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


Domain of the equation: z!=0

z∈R



Domain of the equation: z-5)!=0

z∈R


We get rid of parentheses

z+5/z-9/z+5-5=0

We multiply all the terms by the denominator


z*z+5*z-5*z+5-9=0

We add all the numbers together, and all the variables

z*z-4=0

Wy multiply elements

z^2-4=0

a = 1; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·1·(-4)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*1}=\frac{-4}{2}
=-2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*1}=\frac{4}{2}
=2
$