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3/4n-18=1/2n-4
We move all terms to the left:
3/4n-18-(1/2n-4)=0
Domain of the equation: 4n!=0
n!=0/4
n!=0
n∈R
Domain of the equation: 2n-4)!=0We get rid of parentheses
n∈R
3/4n-1/2n+4-18=0
We calculate fractions
6n/8n^2+(-4n)/8n^2+4-18=0
We add all the numbers together, and all the variables
6n/8n^2+(-4n)/8n^2-14=0
We multiply all the terms by the denominator
6n+(-4n)-14*8n^2=0
Wy multiply elements
-112n^2+6n+(-4n)=0
We get rid of parentheses
-112n^2+6n-4n=0
We add all the numbers together, and all the variables
-112n^2+2n=0
a = -112; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-112)·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$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-112}=\frac{-4}{-224} =1/56 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-112}=\frac{0}{-224} =0 $
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