24=2n^2

Solution for 24=2n^2 equation:

24=2n^2

We move all terms to the left:

24-(2n^2)=0

a = -2; b = 0; c = +24;
Δ = b2-4ac
Δ = 02-4·(-2)·24
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*-2}=\frac{0-8\sqrt{3}}{-4}
=-\frac{8\sqrt{3}}{-4}
=-\frac{2\sqrt{3}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*-2}=\frac{0+8\sqrt{3}}{-4}
=\frac{8\sqrt{3}}{-4}
=\frac{2\sqrt{3}}{-1}
$