5n^2=200

Solution for 5n^2=200 equation:

5n^2=200

We move all terms to the left:

5n^2-(200)=0

a = 5; b = 0; c = -200;
Δ = b2-4ac
Δ = 02-4·5·(-200)
Δ = 4000
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:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{10}}{2*5}=\frac{0-20\sqrt{10}}{10}
=-\frac{20\sqrt{10}}{10}
=-2\sqrt{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{10}}{2*5}=\frac{0+20\sqrt{10}}{10}
=\frac{20\sqrt{10}}{10}
=2\sqrt{10}
$