6n-(6/n)=9

Solution for 6n-(6/n)=9 equation:

6n-(6/n)=9

We move all terms to the left:

6n-(6/n)-(9)=0


Domain of the equation: n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

6n-(+6/n)-9=0

We get rid of parentheses

6n-6/n-9=0

We multiply all the terms by the denominator


6n*n-9*n-6=0

We add all the numbers together, and all the variables

-9n+6n*n-6=0

Wy multiply elements

6n^2-9n-6=0

a = 6; b = -9; c = -6;
Δ = b2-4ac
Δ = -92-4·6·(-6)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*6}=\frac{-6}{12}
=-1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*6}=\frac{24}{12}
=2
$