z^2=675

Solution for z^2=675 equation:

z^2=675

We move all terms to the left:

z^2-(675)=0

a = 1; b = 0; c = -675;
Δ = b2-4ac
Δ = 02-4·1·(-675)
Δ = 2700
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:

$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{3}}{2*1}=\frac{0-30\sqrt{3}}{2}
=-\frac{30\sqrt{3}}{2}
=-15\sqrt{3}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{3}}{2*1}=\frac{0+30\sqrt{3}}{2}
=\frac{30\sqrt{3}}{2}
=15\sqrt{3}
$