3/8n+1-17/6n=-47/12

Solution for 3/8n+1-17/6n=-47/12 equation:

3/8n+1-17/6n=-47/12

We move all terms to the left:

3/8n+1-17/6n-(-47/12)=0


Domain of the equation: 8n!=0

n!=0/8

n!=0

n∈R



Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R


We get rid of parentheses

3/8n-17/6n+1+47/12=0

We calculate fractions


13536n^2/576n^2+216n/576n^2+(-1632n)/576n^2+1=0

We multiply all the terms by the denominator


13536n^2+216n+(-1632n)+1*576n^2=0

Wy multiply elements

13536n^2+576n^2+216n+(-1632n)=0

We get rid of parentheses

13536n^2+576n^2+216n-1632n=0

We add all the numbers together, and all the variables

14112n^2-1416n=0

a = 14112; b = -1416; c = 0;
Δ = b2-4ac
Δ = -14162-4·14112·0
Δ = 2005056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2005056}=1416$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1416)-1416}{2*14112}=\frac{0}{28224}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1416)+1416}{2*14112}=\frac{2832}{28224}
=59/588
$