-31/3n+11/2n=-5/6

Solution for -31/3n+11/2n=-5/6 equation:

-31/3n+11/2n=-5/6

We move all terms to the left:

-31/3n+11/2n-(-5/6)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We get rid of parentheses

-31/3n+11/2n+5/6=0

We calculate fractions


60n^2/216n^2+(-2232n)/216n^2+1188n/216n^2=0

We multiply all the terms by the denominator


60n^2+(-2232n)+1188n=0

We add all the numbers together, and all the variables

60n^2+1188n+(-2232n)=0

We get rid of parentheses

60n^2+1188n-2232n=0

We add all the numbers together, and all the variables

60n^2-1044n=0

a = 60; b = -1044; c = 0;
Δ = b2-4ac
Δ = -10442-4·60·0
Δ = 1089936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089936}=1044$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1044)-1044}{2*60}=\frac{0}{120}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1044)+1044}{2*60}=\frac{2088}{120}
=17+2/5
$