3n^2*2=122

Solution for 3n^2*2=122 equation:

3n^2*2=122

We move all terms to the left:

3n^2*2-(122)=0

Wy multiply elements

6n^2-122=0

a = 6; b = 0; c = -122;
Δ = b2-4ac
Δ = 02-4·6·(-122)
Δ = 2928
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:

$\sqrt{\Delta}=\sqrt{2928}=\sqrt{16*183}=\sqrt{16}*\sqrt{183}=4\sqrt{183}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{183}}{2*6}=\frac{0-4\sqrt{183}}{12}
=-\frac{4\sqrt{183}}{12}
=-\frac{\sqrt{183}}{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{183}}{2*6}=\frac{0+4\sqrt{183}}{12}
=\frac{4\sqrt{183}}{12}
=\frac{\sqrt{183}}{3}
$