5/2n-2n=20

Solution for 5/2n-2n=20 equation:

5/2n-2n=20

We move all terms to the left:

5/2n-2n-(20)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

-2n+5/2n-20=0

We multiply all the terms by the denominator


-2n*2n-20*2n+5=0

Wy multiply elements

-4n^2-40n+5=0

a = -4; b = -40; c = +5;
Δ = b2-4ac
Δ = -402-4·(-4)·5
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{105}}{2*-4}=\frac{40-4\sqrt{105}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{105}}{2*-4}=\frac{40+4\sqrt{105}}{-8}
$