z+4/z=-5

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

z+4/z=-5

We move all terms to the left:

z+4/z-(-5)=0


Domain of the equation: z!=0

z∈R


We add all the numbers together, and all the variables

z+4/z+5=0

We multiply all the terms by the denominator


z*z+5*z+4=0

We add all the numbers together, and all the variables

5z+z*z+4=0

Wy multiply elements

z^2+5z+4=0

a = 1; b = 5; c = +4;
Δ = b2-4ac
Δ = 52-4·1·4
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3}{2*1}=\frac{-8}{2}
=-4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3}{2*1}=\frac{-2}{2}
=-1
$