-45n^2+9=0

Solution for -45n^2+9=0 equation:

-45n^2+9=0

a = -45; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-45)·9
Δ = 1620
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{5}}{2*-45}=\frac{0-18\sqrt{5}}{-90}
=-\frac{18\sqrt{5}}{-90}
=-\frac{\sqrt{5}}{-5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{5}}{2*-45}=\frac{0+18\sqrt{5}}{-90}
=\frac{18\sqrt{5}}{-90}
=\frac{\sqrt{5}}{-5}
$