25z^2-45=0

Solution for 25z^2-45=0 equation:

25z^2-45=0

a = 25; b = 0; c = -45;
Δ = b2-4ac
Δ = 02-4·25·(-45)
Δ = 4500
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:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{5}}{2*25}=\frac{0-30\sqrt{5}}{50}
=-\frac{30\sqrt{5}}{50}
=-\frac{3\sqrt{5}}{5}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{5}}{2*25}=\frac{0+30\sqrt{5}}{50}
=\frac{30\sqrt{5}}{50}
=\frac{3\sqrt{5}}{5}
$