(z-8)(z+2)-264=0

Solution for (z-8)(z+2)-264=0 equation:

(z-8)(z+2)-264=0

We multiply parentheses ..

(+z^2+2z-8z-16)-264=0

We get rid of parentheses

z^2+2z-8z-16-264=0

We add all the numbers together, and all the variables

z^2-6z-280=0

a = 1; b = -6; c = -280;
Δ = b2-4ac
Δ = -62-4·1·(-280)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-34}{2*1}=\frac{-28}{2}
=-14
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+34}{2*1}=\frac{40}{2}
=20
$