z^2-423=-99

Solution for z^2-423=-99 equation:

z^2-423=-99

We move all terms to the left:

z^2-423-(-99)=0

We add all the numbers together, and all the variables

z^2-324=0

a = 1; b = 0; c = -324;
Δ = b2-4ac
Δ = 02-4·1·(-324)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36}{2*1}=\frac{-36}{2}
=-18
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36}{2*1}=\frac{36}{2}
=18
$