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1/9n+2/3n=4
We move all terms to the left:
1/9n+2/3n-(4)=0
Domain of the equation: 9n!=0
n!=0/9
n!=0
n∈R
Domain of the equation: 3n!=0We calculate fractions
n!=0/3
n!=0
n∈R
3n/27n^2+18n/27n^2-4=0
We multiply all the terms by the denominator
3n+18n-4*27n^2=0
We add all the numbers together, and all the variables
21n-4*27n^2=0
Wy multiply elements
-108n^2+21n=0
a = -108; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-108)·0
Δ = 441
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{441}=21$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-108}=\frac{-42}{-216} =7/36 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-108}=\frac{0}{-216} =0 $
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