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1/2n-1/4n=2
We move all terms to the left:
1/2n-1/4n-(2)=0
Domain of the equation: 2n!=0
n!=0/2
n!=0
n∈R
Domain of the equation: 4n!=0We calculate fractions
n!=0/4
n!=0
n∈R
4n/8n^2+(-2n)/8n^2-2=0
We multiply all the terms by the denominator
4n+(-2n)-2*8n^2=0
Wy multiply elements
-16n^2+4n+(-2n)=0
We get rid of parentheses
-16n^2+4n-2n=0
We add all the numbers together, and all the variables
-16n^2+2n=0
a = -16; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-16)·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$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-16}=\frac{-4}{-32} =1/8 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-16}=\frac{0}{-32} =0 $
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