1/4n+5=11/2n

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Solution for 1/4n+5=11/2n equation:



1/4n+5=11/2n
We move all terms to the left:
1/4n+5-(11/2n)=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-(+11/2n)+5=0
We get rid of parentheses
1/4n-11/2n+5=0
We calculate fractions
2n/8n^2+(-44n)/8n^2+5=0
We multiply all the terms by the denominator
2n+(-44n)+5*8n^2=0
Wy multiply elements
40n^2+2n+(-44n)=0
We get rid of parentheses
40n^2+2n-44n=0
We add all the numbers together, and all the variables
40n^2-42n=0
a = 40; b = -42; c = 0;
Δ = b2-4ac
Δ = -422-4·40·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-42}{2*40}=\frac{0}{80} =0 $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+42}{2*40}=\frac{84}{80} =1+1/20 $

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