180n^2=3060

Solution for 180n^2=3060 equation:

180n^2=3060

We move all terms to the left:

180n^2-(3060)=0

a = 180; b = 0; c = -3060;
Δ = b2-4ac
Δ = 02-4·180·(-3060)
Δ = 2203200
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:

$\sqrt{\Delta}=\sqrt{2203200}=\sqrt{129600*17}=\sqrt{129600}*\sqrt{17}=360\sqrt{17}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-360\sqrt{17}}{2*180}=\frac{0-360\sqrt{17}}{360}
=-\frac{360\sqrt{17}}{360}
=-\sqrt{17}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+360\sqrt{17}}{2*180}=\frac{0+360\sqrt{17}}{360}
=\frac{360\sqrt{17}}{360}
=\sqrt{17}
$