n2=5020

Solution for n2=5020 equation:

n2=5020

We move all terms to the left:

n2-(5020)=0

We add all the numbers together, and all the variables

n^2-5020=0

a = 1; b = 0; c = -5020;
Δ = b2-4ac
Δ = 02-4·1·(-5020)
Δ = 20080
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:

$\sqrt{\Delta}=\sqrt{20080}=\sqrt{16*1255}=\sqrt{16}*\sqrt{1255}=4\sqrt{1255}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{1255}}{2*1}=\frac{0-4\sqrt{1255}}{2}
=-\frac{4\sqrt{1255}}{2}
=-2\sqrt{1255}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{1255}}{2*1}=\frac{0+4\sqrt{1255}}{2}
=\frac{4\sqrt{1255}}{2}
=2\sqrt{1255}
$