z-3/z+3=z/z+5

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

z-3/z+3=z/z+5

We move all terms to the left:

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

Fractions to decimals

-3/z+z-5+3+1=0

We multiply all the terms by the denominator


z*z-5*z+3*z+1*z-3=0

We add all the numbers together, and all the variables

-1z+z*z-3=0

Wy multiply elements

z^2-1z-3=0

a = 1; b = -1; c = -3;
Δ = b2-4ac
Δ = -12-4·1·(-3)
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{13}}{2*1}=\frac{1-\sqrt{13}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{13}}{2*1}=\frac{1+\sqrt{13}}{2}
$