z2+(z+5)2=13

Solution for z2+(z+5)2=13 equation:

z2+(z+5)2=13

We move all terms to the left:

z2+(z+5)2-(13)=0

We add all the numbers together, and all the variables

z^2+(z+5)2-13=0

We multiply parentheses

z^2+2z+10-13=0

We add all the numbers together, and all the variables

z^2+2z-3=0

a = 1; b = 2; c = -3;
Δ = b2-4ac
Δ = 22-4·1·(-3)
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{-(2)-4}{2*1}=\frac{-6}{2}
=-3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4}{2*1}=\frac{2}{2}
=1
$