N(t)=100t-5t^2

Solution for N(t)=100t-5t^2 equation:

(N)=100N-5N^2

We move all terms to the left:

(N)-(100N-5N^2)=0

We get rid of parentheses

5N^2-100N+N=0

We add all the numbers together, and all the variables

5N^2-99N=0

a = 5; b = -99; c = 0;
Δ = b2-4ac
Δ = -992-4·5·0
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-99}{2*5}=\frac{0}{10}
=0
$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+99}{2*5}=\frac{198}{10}
=19+4/5
$