-31/3n+1/3+11/2n=-51/6

Solution for -31/3n+1/3+11/2n=-51/6 equation:

-31/3n+1/3+11/2n=-51/6

We move all terms to the left:

-31/3n+1/3+11/2n-(-51/6)=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+1/3+51/6=0

We calculate fractions


1836n^2/324n^2+(-2232n)/324n^2+1782n/324n^2+72n/324n^2=0

We multiply all the terms by the denominator


1836n^2+(-2232n)+1782n+72n=0

We add all the numbers together, and all the variables

1836n^2+1854n+(-2232n)=0

We get rid of parentheses

1836n^2+1854n-2232n=0

We add all the numbers together, and all the variables

1836n^2-378n=0

a = 1836; b = -378; c = 0;
Δ = b2-4ac
Δ = -3782-4·1836·0
Δ = 142884
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{142884}=378$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-378)-378}{2*1836}=\frac{0}{3672}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-378)+378}{2*1836}=\frac{756}{3672}
=7/34
$