3+6n^2=24

Solution for 3+6n^2=24 equation:

3+6n^2=24

We move all terms to the left:

3+6n^2-(24)=0

We add all the numbers together, and all the variables

6n^2-21=0

a = 6; b = 0; c = -21;
Δ = b2-4ac
Δ = 02-4·6·(-21)
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{14}}{2*6}=\frac{0-6\sqrt{14}}{12}
=-\frac{6\sqrt{14}}{12}
=-\frac{\sqrt{14}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{14}}{2*6}=\frac{0+6\sqrt{14}}{12}
=\frac{6\sqrt{14}}{12}
=\frac{\sqrt{14}}{2}
$