1/2n-3=2/3n

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Solution for 1/2n-3=2/3n equation:



1/2n-3=2/3n
We move all terms to the left:
1/2n-3-(2/3n)=0
Domain of the equation: 2n!=0
n!=0/2
n!=0
n∈R
Domain of the equation: 3n)!=0
n!=0/1
n!=0
n∈R
We add all the numbers together, and all the variables
1/2n-(+2/3n)-3=0
We get rid of parentheses
1/2n-2/3n-3=0
We calculate fractions
3n/6n^2+(-4n)/6n^2-3=0
We multiply all the terms by the denominator
3n+(-4n)-3*6n^2=0
Wy multiply elements
-18n^2+3n+(-4n)=0
We get rid of parentheses
-18n^2+3n-4n=0
We add all the numbers together, and all the variables
-18n^2-1n=0
a = -18; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-18)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-18}=\frac{0}{-36} =0 $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-18}=\frac{2}{-36} =-1/18 $

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