1/4n+1=1/2n-2

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Solution for 1/4n+1=1/2n-2 equation:



1/4n+1=1/2n-2
We move all terms to the left:
1/4n+1-(1/2n-2)=0
Domain of the equation: 4n!=0
n!=0/4
n!=0
n∈R
Domain of the equation: 2n-2)!=0
n∈R
We get rid of parentheses
1/4n-1/2n+2+1=0
We calculate fractions
2n/8n^2+(-4n)/8n^2+2+1=0
We add all the numbers together, and all the variables
2n/8n^2+(-4n)/8n^2+3=0
We multiply all the terms by the denominator
2n+(-4n)+3*8n^2=0
Wy multiply elements
24n^2+2n+(-4n)=0
We get rid of parentheses
24n^2+2n-4n=0
We add all the numbers together, and all the variables
24n^2-2n=0
a = 24; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·24·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*24}=\frac{0}{48} =0 $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*24}=\frac{4}{48} =1/12 $

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