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7/6n+1/2n=5
We move all terms to the left:
7/6n+1/2n-(5)=0
Domain of the equation: 6n!=0
n!=0/6
n!=0
n∈R
Domain of the equation: 2n!=0We calculate fractions
n!=0/2
n!=0
n∈R
14n/12n^2+6n/12n^2-5=0
We multiply all the terms by the denominator
14n+6n-5*12n^2=0
We add all the numbers together, and all the variables
20n-5*12n^2=0
Wy multiply elements
-60n^2+20n=0
a = -60; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-60)·0
Δ = 400
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{400}=20$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-60}=\frac{-40}{-120} =1/3 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-60}=\frac{0}{-120} =0 $
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