z2=8-z=-24

Solution for z2=8-z=-24 equation:

z2=8-z=-24

We move all terms to the left:

z2-(8-z)=0

We add all the numbers together, and all the variables

z2-(-1z+8)=0

We add all the numbers together, and all the variables

z^2-(-1z+8)=0

We get rid of parentheses

z^2+1z-8=0

We add all the numbers together, and all the variables

z^2+z-8=0

a = 1; b = 1; c = -8;
Δ = b2-4ac
Δ = 12-4·1·(-8)
Δ = 33
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{33}}{2*1}=\frac{-1-\sqrt{33}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{33}}{2*1}=\frac{-1+\sqrt{33}}{2}
$