6n/n^2+5=1

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

6n/n^2+5=1

We move all terms to the left:

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


Domain of the equation: n^2!=0

n^2!=0/

n^2!=√0

n!=0

n∈R


We add all the numbers together, and all the variables

6n/n^2+4=0

We multiply all the terms by the denominator


6n+4*n^2=0

We add all the numbers together, and all the variables

4n^2+6n=0

a = 4; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·4·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*4}=\frac{-12}{8}
=-1+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*4}=\frac{0}{8}
=0
$