-z^2+45+12z=0

Solution for -z^2+45+12z=0 equation:

-z^2+45+12z=0

We add all the numbers together, and all the variables

-1z^2+12z+45=0

a = -1; b = 12; c = +45;
Δ = b2-4ac
Δ = 122-4·(-1)·45
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-18}{2*-1}=\frac{-30}{-2}
=+15
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+18}{2*-1}=\frac{6}{-2}
=-3
$