0=z^2+18z+80

Solution for 0=z^2+18z+80 equation:

0=z^2+18z+80

We move all terms to the left:

0-(z^2+18z+80)=0

We add all the numbers together, and all the variables

-(z^2+18z+80)=0

We get rid of parentheses

-z^2-18z-80=0

We add all the numbers together, and all the variables

-1z^2-18z-80=0

a = -1; b = -18; c = -80;
Δ = b2-4ac
Δ = -182-4·(-1)·(-80)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2}{2*-1}=\frac{16}{-2}
=-8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2}{2*-1}=\frac{20}{-2}
=-10
$