2/3n+5=1/2n-9

Solution for 2/3n+5=1/2n-9 equation:

2/3n+5=1/2n-9

We move all terms to the left:

2/3n+5-(1/2n-9)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 2n-9)!=0

n∈R


We get rid of parentheses

2/3n-1/2n+9+5=0

We calculate fractions


4n/6n^2+(-3n)/6n^2+9+5=0

We add all the numbers together, and all the variables

4n/6n^2+(-3n)/6n^2+14=0

We multiply all the terms by the denominator


4n+(-3n)+14*6n^2=0

Wy multiply elements

84n^2+4n+(-3n)=0

We get rid of parentheses

84n^2+4n-3n=0

We add all the numbers together, and all the variables

84n^2+n=0

a = 84; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·84·0
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*84}=\frac{-2}{168}
=-1/84
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*84}=\frac{0}{168}
=0
$