50+100n=n2

Solution for 50+100n=n2 equation:

50+100n=n2

We move all terms to the left:

50+100n-(n2)=0

We add all the numbers together, and all the variables

-1n^2+100n+50=0

a = -1; b = 100; c = +50;
Δ = b2-4ac
Δ = 1002-4·(-1)·50
Δ = 10200
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:

$\sqrt{\Delta}=\sqrt{10200}=\sqrt{100*102}=\sqrt{100}*\sqrt{102}=10\sqrt{102}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-10\sqrt{102}}{2*-1}=\frac{-100-10\sqrt{102}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+10\sqrt{102}}{2*-1}=\frac{-100+10\sqrt{102}}{-2}
$