3n+6n-9/n-1=6

Solution for 3n+6n-9/n-1=6 equation:

3n+6n-9/n-1=6

We move all terms to the left:

3n+6n-9/n-1-(6)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

9n-9/n-7=0

We multiply all the terms by the denominator


9n*n-7*n-9=0

We add all the numbers together, and all the variables

-7n+9n*n-9=0

Wy multiply elements

9n^2-7n-9=0

a = 9; b = -7; c = -9;
Δ = b2-4ac
Δ = -72-4·9·(-9)
Δ = 373
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{373}}{2*9}=\frac{7-\sqrt{373}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{373}}{2*9}=\frac{7+\sqrt{373}}{18}
$