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1/2n+5=3/4n
We move all terms to the left:
1/2n+5-(3/4n)=0
Domain of the equation: 2n!=0
n!=0/2
n!=0
n∈R
Domain of the equation: 4n)!=0We add all the numbers together, and all the variables
n!=0/1
n!=0
n∈R
1/2n-(+3/4n)+5=0
We get rid of parentheses
1/2n-3/4n+5=0
We calculate fractions
4n/8n^2+(-6n)/8n^2+5=0
We multiply all the terms by the denominator
4n+(-6n)+5*8n^2=0
Wy multiply elements
40n^2+4n+(-6n)=0
We get rid of parentheses
40n^2+4n-6n=0
We add all the numbers together, and all the variables
40n^2-2n=0
a = 40; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·40·0
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$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*40}=\frac{0}{80} =0 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*40}=\frac{4}{80} =1/20 $
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