82=z2

Solution for 82=z2 equation:

82=z2

We move all terms to the left:

82-(z2)=0

We add all the numbers together, and all the variables

-1z^2+82=0

a = -1; b = 0; c = +82;
Δ = b2-4ac
Δ = 02-4·(-1)·82
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{82}}{2*-1}=\frac{0-2\sqrt{82}}{-2}
=-\frac{2\sqrt{82}}{-2}
=-\frac{\sqrt{82}}{-1}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{82}}{2*-1}=\frac{0+2\sqrt{82}}{-2}
=\frac{2\sqrt{82}}{-2}
=\frac{\sqrt{82}}{-1}
$