N(t)=20t/t+2

Solution for N(t)=20t/t+2 equation:

(N)=20N/N+2

We move all terms to the left:

(N)-(20N/N+2)=0


Domain of the equation: N+2)!=0

N∈R


We get rid of parentheses

N-20N/N-2=0

We multiply all the terms by the denominator


N*N-20N-2*N=0

We add all the numbers together, and all the variables

-22N+N*N=0

Wy multiply elements

N^2-22N=0

a = 1; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·1·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*1}=\frac{0}{2}
=0
$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*1}=\frac{44}{2}
=22
$