-5z-5=z^2

Solution for -5z-5=z^2 equation:

-5z-5=z^2

We move all terms to the left:

-5z-5-(z^2)=0

determiningTheFunctionDomain
-z^2-5z-5=0

We add all the numbers together, and all the variables

-1z^2-5z-5=0

a = -1; b = -5; c = -5;
Δ = b2-4ac
Δ = -52-4·(-1)·(-5)
Δ = 5
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{5}}{2*-1}=\frac{5-\sqrt{5}}{-2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{5}}{2*-1}=\frac{5+\sqrt{5}}{-2}
$