z(z-13)=-36

Solution for z(z-13)=-36 equation:

z(z-13)=-36

We move all terms to the left:

z(z-13)-(-36)=0

We add all the numbers together, and all the variables

z(z-13)+36=0

We multiply parentheses

z^2-13z+36=0

a = 1; b = -13; c = +36;
Δ = b2-4ac
Δ = -132-4·1·36
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-5}{2*1}=\frac{8}{2}
=4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+5}{2*1}=\frac{18}{2}
=9
$