2/3n+n=15

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Solution for 2/3n+n=15 equation:



2/3n+n=15
We move all terms to the left:
2/3n+n-(15)=0
Domain of the equation: 3n!=0
n!=0/3
n!=0
n∈R
We add all the numbers together, and all the variables
n+2/3n-15=0
We multiply all the terms by the denominator
n*3n-15*3n+2=0
Wy multiply elements
3n^2-45n+2=0
a = 3; b = -45; c = +2;
Δ = b2-4ac
Δ = -452-4·3·2
Δ = 2001
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{-(-45)-\sqrt{2001}}{2*3}=\frac{45-\sqrt{2001}}{6} $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2001}}{2*3}=\frac{45+\sqrt{2001}}{6} $

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