-z(z-5)+3=-5

Solution for -z(z-5)+3=-5 equation:

-z(z-5)+3=-5

We move all terms to the left:

-z(z-5)+3-(-5)=0

We add all the numbers together, and all the variables

-z(z-5)+8=0

We multiply parentheses

-z^2+5z+8=0

We add all the numbers together, and all the variables

-1z^2+5z+8=0

a = -1; b = 5; c = +8;
Δ = b2-4ac
Δ = 52-4·(-1)·8
Δ = 57
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{57}}{2*-1}=\frac{-5-\sqrt{57}}{-2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{57}}{2*-1}=\frac{-5+\sqrt{57}}{-2}
$