5=6n-2/n+1

Solution for 5=6n-2/n+1 equation:

5=6n-2/n+1

We move all terms to the left:

5-(6n-2/n+1)=0


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

n∈R


We get rid of parentheses

-6n+2/n-1+5=0

We multiply all the terms by the denominator


-6n*n-1*n+5*n+2=0

We add all the numbers together, and all the variables

4n-6n*n+2=0

Wy multiply elements

-6n^2+4n+2=0

a = -6; b = 4; c = +2;
Δ = b2-4ac
Δ = 42-4·(-6)·2
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*-6}=\frac{-12}{-12}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*-6}=\frac{4}{-12}
=-1/3
$