1/3n+2/5n=1100

Solution for 1/3n+2/5n=1100 equation:

1/3n+2/5n=1100

We move all terms to the left:

1/3n+2/5n-(1100)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We calculate fractions


5n/15n^2+6n/15n^2-1100=0

We multiply all the terms by the denominator


5n+6n-1100*15n^2=0

We add all the numbers together, and all the variables

11n-1100*15n^2=0

Wy multiply elements

-16500n^2+11n=0

a = -16500; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-16500)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-16500}=\frac{-22}{-33000}
=1/1500
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-16500}=\frac{0}{-33000}
=0
$