n^2-2n=100

Solution for n^2-2n=100 equation:

n^2-2n=100

We move all terms to the left:

n^2-2n-(100)=0

a = 1; b = -2; c = -100;
Δ = b2-4ac
Δ = -22-4·1·(-100)
Δ = 404
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:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{101}}{2*1}=\frac{2-2\sqrt{101}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{101}}{2*1}=\frac{2+2\sqrt{101}}{2}
$