0=z2-z-2

Solution for 0=z2-z-2 equation:

0=z2-z-2

We move all terms to the left:

0-(z2-z-2)=0

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-z^2+1z+2=0

We add all the numbers together, and all the variables

-1z^2+z+2=0

a = -1; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-1)·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3}{2*-1}=\frac{-4}{-2}
=+2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3}{2*-1}=\frac{2}{-2}
=-1
$