z^2+8z=-7

Solution for z^2+8z=-7 equation:

z^2+8z=-7

We move all terms to the left:

z^2+8z-(-7)=0

We add all the numbers together, and all the variables

z^2+8z+7=0

a = 1; b = 8; c = +7;
Δ = b2-4ac
Δ = 82-4·1·7
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6}{2*1}=\frac{-14}{2}
=-7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6}{2*1}=\frac{-2}{2}
=-1
$