3n^2=150

Solution for 3n^2=150 equation:

3n^2=150

We move all terms to the left:

3n^2-(150)=0

a = 3; b = 0; c = -150;
Δ = b2-4ac
Δ = 02-4·3·(-150)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{2}}{2*3}=\frac{0-30\sqrt{2}}{6}
=-\frac{30\sqrt{2}}{6}
=-5\sqrt{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{2}}{2*3}=\frac{0+30\sqrt{2}}{6}
=\frac{30\sqrt{2}}{6}
=5\sqrt{2}
$