z^2=24

Solution for z^2=24 equation:

z^2=24

We move all terms to the left:

z^2-(24)=0

a = 1; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·1·(-24)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*1}=\frac{0-4\sqrt{6}}{2}
=-\frac{4\sqrt{6}}{2}
=-2\sqrt{6}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*1}=\frac{0+4\sqrt{6}}{2}
=\frac{4\sqrt{6}}{2}
=2\sqrt{6}
$