n^2-2=10000

Solution for n^2-2=10000 equation:

n^2-2=10000

We move all terms to the left:

n^2-2-(10000)=0

We add all the numbers together, and all the variables

n^2-10002=0

a = 1; b = 0; c = -10002;
Δ = b2-4ac
Δ = 02-4·1·(-10002)
Δ = 40008
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:

$\sqrt{\Delta}=\sqrt{40008}=\sqrt{4*10002}=\sqrt{4}*\sqrt{10002}=2\sqrt{10002}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10002}}{2*1}=\frac{0-2\sqrt{10002}}{2}
=-\frac{2\sqrt{10002}}{2}
=-\sqrt{10002}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10002}}{2*1}=\frac{0+2\sqrt{10002}}{2}
=\frac{2\sqrt{10002}}{2}
=\sqrt{10002}
$