3n^2=41

Solution for 3n^2=41 equation:

3n^2=41

We move all terms to the left:

3n^2-(41)=0

a = 3; b = 0; c = -41;
Δ = b2-4ac
Δ = 02-4·3·(-41)
Δ = 492
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:

$\sqrt{\Delta}=\sqrt{492}=\sqrt{4*123}=\sqrt{4}*\sqrt{123}=2\sqrt{123}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{123}}{2*3}=\frac{0-2\sqrt{123}}{6}
=-\frac{2\sqrt{123}}{6}
=-\frac{\sqrt{123}}{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{123}}{2*3}=\frac{0+2\sqrt{123}}{6}
=\frac{2\sqrt{123}}{6}
=\frac{\sqrt{123}}{3}
$