n^2-n=10000

Solution for n^2-n=10000 equation:

n^2-n=10000

We move all terms to the left:

n^2-n-(10000)=0

We add all the numbers together, and all the variables

n^2-1n-10000=0

a = 1; b = -1; c = -10000;
Δ = b2-4ac
Δ = -12-4·1·(-10000)
Δ = 40001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{40001}}{2*1}=\frac{1-\sqrt{40001}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{40001}}{2*1}=\frac{1+\sqrt{40001}}{2}
$