3n2=302

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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} $

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