9=5z^2

Solution for 9=5z^2 equation:

9=5z^2

We move all terms to the left:

9-(5z^2)=0

a = -5; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-5)·9
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*-5}=\frac{0-6\sqrt{5}}{-10}
=-\frac{6\sqrt{5}}{-10}
=-\frac{3\sqrt{5}}{-5}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*-5}=\frac{0+6\sqrt{5}}{-10}
=\frac{6\sqrt{5}}{-10}
=\frac{3\sqrt{5}}{-5}
$