3/n+1=4+n+4

Solution for 3/n+1=4+n+4 equation:

3/n+1=4+n+4

We move all terms to the left:

3/n+1-(4+n+4)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

3/n-(n+8)+1=0

We get rid of parentheses

3/n-n-8+1=0

We multiply all the terms by the denominator


-n*n-8*n+1*n+3=0

We add all the numbers together, and all the variables

-7n-n*n+3=0

Wy multiply elements

-1n^2-7n+3=0

a = -1; b = -7; c = +3;
Δ = b2-4ac
Δ = -72-4·(-1)·3
Δ = 61
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{61}}{2*-1}=\frac{7-\sqrt{61}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{61}}{2*-1}=\frac{7+\sqrt{61}}{-2}
$