3n^2=1000

Solution for 3n^2=1000 equation:

3n^2=1000

We move all terms to the left:

3n^2-(1000)=0

a = 3; b = 0; c = -1000;
Δ = b2-4ac
Δ = 02-4·3·(-1000)
Δ = 12000
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:

$\sqrt{\Delta}=\sqrt{12000}=\sqrt{400*30}=\sqrt{400}*\sqrt{30}=20\sqrt{30}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{30}}{2*3}=\frac{0-20\sqrt{30}}{6}
=-\frac{20\sqrt{30}}{6}
=-\frac{10\sqrt{30}}{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{30}}{2*3}=\frac{0+20\sqrt{30}}{6}
=\frac{20\sqrt{30}}{6}
=\frac{10\sqrt{30}}{3}
$