z2-27z-72=0

Solution for z2-27z-72=0 equation:

z2-27z-72=0

We add all the numbers together, and all the variables

z^2-27z-72=0

a = 1; b = -27; c = -72;
Δ = b2-4ac
Δ = -272-4·1·(-72)
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{113}}{2*1}=\frac{27-3\sqrt{113}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{113}}{2*1}=\frac{27+3\sqrt{113}}{2}
$