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1/2n+7=3/4n+9
We move all terms to the left:
1/2n+7-(3/4n+9)=0
Domain of the equation: 2n!=0
n!=0/2
n!=0
n∈R
Domain of the equation: 4n+9)!=0We get rid of parentheses
n∈R
1/2n-3/4n-9+7=0
We calculate fractions
4n/8n^2+(-6n)/8n^2-9+7=0
We add all the numbers together, and all the variables
4n/8n^2+(-6n)/8n^2-2=0
We multiply all the terms by the denominator
4n+(-6n)-2*8n^2=0
Wy multiply elements
-16n^2+4n+(-6n)=0
We get rid of parentheses
-16n^2+4n-6n=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$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-16}=\frac{0}{-32} =0 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-16}=\frac{4}{-32} =-1/8 $
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