9n^2-5=0

Solution for 9n^2-5=0 equation:

9n^2-5=0

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

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*9}=\frac{0-6\sqrt{5}}{18}
=-\frac{6\sqrt{5}}{18}
=-\frac{\sqrt{5}}{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*9}=\frac{0+6\sqrt{5}}{18}
=\frac{6\sqrt{5}}{18}
=\frac{\sqrt{5}}{3}
$