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-2/3n+8=1/2n+2
We move all terms to the left:
-2/3n+8-(1/2n+2)=0
Domain of the equation: 3n!=0
n!=0/3
n!=0
n∈R
Domain of the equation: 2n+2)!=0We get rid of parentheses
n∈R
-2/3n-1/2n-2+8=0
We calculate fractions
(-4n)/6n^2+(-3n)/6n^2-2+8=0
We add all the numbers together, and all the variables
(-4n)/6n^2+(-3n)/6n^2+6=0
We multiply all the terms by the denominator
(-4n)+(-3n)+6*6n^2=0
Wy multiply elements
36n^2+(-4n)+(-3n)=0
We get rid of parentheses
36n^2-4n-3n=0
We add all the numbers together, and all the variables
36n^2-7n=0
a = 36; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·36·0
Δ = 49
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{49}=7$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*36}=\frac{0}{72} =0 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*36}=\frac{14}{72} =7/36 $
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