3n2=302

Solution for 3n2=302 equation:

3n^2=302

We move all terms to the left:

3n^2-(302)=0

a = 3; b = 0; c = -302;
Δ = b2-4ac
Δ = 02-4·3·(-302)
Δ = 3624
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:

$\sqrt{\Delta}=\sqrt{3624}=\sqrt{4*906}=\sqrt{4}*\sqrt{906}=2\sqrt{906}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{906}}{2*3}=\frac{0-2\sqrt{906}}{6}
=-\frac{2\sqrt{906}}{6}
=-\frac{\sqrt{906}}{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{906}}{2*3}=\frac{0+2\sqrt{906}}{6}
=\frac{2\sqrt{906}}{6}
=\frac{\sqrt{906}}{3}
$