5/2n+1/6n=-16/7

Solution for 5/2n+1/6n=-16/7 equation:

5/2n+1/6n=-16/7

We move all terms to the left:

5/2n+1/6n-(-16/7)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R


We get rid of parentheses

5/2n+1/6n+16/7=0

We calculate fractions


1152n^2/588n^2+1470n/588n^2+98n/588n^2=0

We multiply all the terms by the denominator


1152n^2+1470n+98n=0

We add all the numbers together, and all the variables

1152n^2+1568n=0

a = 1152; b = 1568; c = 0;
Δ = b2-4ac
Δ = 15682-4·1152·0
Δ = 2458624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2458624}=1568$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1568)-1568}{2*1152}=\frac{-3136}{2304}
=-1+13/36
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1568)+1568}{2*1152}=\frac{0}{2304}
=0
$