5n^2-192=0

Solution for 5n^2-192=0 equation:

5n^2-192=0

a = 5; b = 0; c = -192;
Δ = b2-4ac
Δ = 02-4·5·(-192)
Δ = 3840
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:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{15}}{2*5}=\frac{0-16\sqrt{15}}{10}
=-\frac{16\sqrt{15}}{10}
=-\frac{8\sqrt{15}}{5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{15}}{2*5}=\frac{0+16\sqrt{15}}{10}
=\frac{16\sqrt{15}}{10}
=\frac{8\sqrt{15}}{5}
$