z^2=66

Solution for z^2=66 equation:

z^2=66

We move all terms to the left:

z^2-(66)=0

a = 1; b = 0; c = -66;
Δ = b2-4ac
Δ = 02-4·1·(-66)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{66}}{2*1}=\frac{0-2\sqrt{66}}{2}
=-\frac{2\sqrt{66}}{2}
=-\sqrt{66}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{66}}{2*1}=\frac{0+2\sqrt{66}}{2}
=\frac{2\sqrt{66}}{2}
=\sqrt{66}
$