1/4n+5=51/2n

Solution for 1/4n+5=51/2n equation:

1/4n+5=51/2n

We move all terms to the left:

1/4n+5-(51/2n)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

1/4n-(+51/2n)+5=0

We get rid of parentheses

1/4n-51/2n+5=0

We calculate fractions


2n/8n^2+(-204n)/8n^2+5=0

We multiply all the terms by the denominator


2n+(-204n)+5*8n^2=0

Wy multiply elements

40n^2+2n+(-204n)=0

We get rid of parentheses

40n^2+2n-204n=0

We add all the numbers together, and all the variables

40n^2-202n=0

a = 40; b = -202; c = 0;
Δ = b2-4ac
Δ = -2022-4·40·0
Δ = 40804
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40804}=202$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-202)-202}{2*40}=\frac{0}{80}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-202)+202}{2*40}=\frac{404}{80}
=5+1/20
$