1/2n+1/3n=5

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

1/2n+1/3n=5

We move all terms to the left:

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


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We calculate fractions


3n/6n^2+2n/6n^2-5=0

We multiply all the terms by the denominator


3n+2n-5*6n^2=0

We add all the numbers together, and all the variables

5n-5*6n^2=0

Wy multiply elements

-30n^2+5n=0

a = -30; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-30)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-30}=\frac{-10}{-60}
=1/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-30}=\frac{0}{-60}
=0
$