6n^2=168

Solution for 6n^2=168 equation:

6n^2=168

We move all terms to the left:

6n^2-(168)=0

a = 6; b = 0; c = -168;
Δ = b2-4ac
Δ = 02-4·6·(-168)
Δ = 4032
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:

$\sqrt{\Delta}=\sqrt{4032}=\sqrt{576*7}=\sqrt{576}*\sqrt{7}=24\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{7}}{2*6}=\frac{0-24\sqrt{7}}{12}
=-\frac{24\sqrt{7}}{12}
=-2\sqrt{7}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{7}}{2*6}=\frac{0+24\sqrt{7}}{12}
=\frac{24\sqrt{7}}{12}
=2\sqrt{7}
$