z^2+8z=27

Solution for z^2+8z=27 equation:

z^2+8z=27

We move all terms to the left:

z^2+8z-(27)=0

a = 1; b = 8; c = -27;
Δ = b2-4ac
Δ = 82-4·1·(-27)
Δ = 172
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{43}}{2*1}=\frac{-8-2\sqrt{43}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{43}}{2*1}=\frac{-8+2\sqrt{43}}{2}
$