z2=593

Solution for z2=593 equation:

z2=593

We move all terms to the left:

z2-(593)=0

We add all the numbers together, and all the variables

z^2-593=0

a = 1; b = 0; c = -593;
Δ = b2-4ac
Δ = 02-4·1·(-593)
Δ = 2372
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2372}=\sqrt{4*593}=\sqrt{4}*\sqrt{593}=2\sqrt{593}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{593}}{2*1}=\frac{0-2\sqrt{593}}{2}
=-\frac{2\sqrt{593}}{2}
=-\sqrt{593}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{593}}{2*1}=\frac{0+2\sqrt{593}}{2}
=\frac{2\sqrt{593}}{2}
=\sqrt{593}
$