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2/3n+n=5
We move all terms to the left:
2/3n+n-(5)=0
Domain of the equation: 3n!=0We add all the numbers together, and all the variables
n!=0/3
n!=0
n∈R
n+2/3n-5=0
We multiply all the terms by the denominator
n*3n-5*3n+2=0
Wy multiply elements
3n^2-15n+2=0
a = 3; b = -15; c = +2;
Δ = b2-4ac
Δ = -152-4·3·2
Δ = 201
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{201}}{2*3}=\frac{15-\sqrt{201}}{6} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{201}}{2*3}=\frac{15+\sqrt{201}}{6} $
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