N+n/2+2n/n+3=20

Solution for N+n/2+2n/n+3=20 equation:

+N/2+2N/N+3=20

We move all terms to the left:

+N/2+2N/N+3-(20)=0


Domain of the equation: N!=0

N∈R


We add all the numbers together, and all the variables

N/2+2N/N-17=0

We calculate fractions


N^2/2N+4N/2N-17=0

We multiply all the terms by the denominator


N^2+4N-17*2N=0

Wy multiply elements

N^2+4N-34N=0

We add all the numbers together, and all the variables

N^2-30N=0

a = 1; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·1·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*1}=\frac{0}{2}
=0
$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*1}=\frac{60}{2}
=30
$