7=3n+2/n+1

Solution for 7=3n+2/n+1 equation:

7=3n+2/n+1

We move all terms to the left:

7-(3n+2/n+1)=0


Domain of the equation: n+1)!=0

n∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

6n-3n*n-2=0

Wy multiply elements

-3n^2+6n-2=0

a = -3; b = 6; c = -2;
Δ = b2-4ac
Δ = 62-4·(-3)·(-2)
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{3}}{2*-3}=\frac{-6-2\sqrt{3}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{3}}{2*-3}=\frac{-6+2\sqrt{3}}{-6}
$