3n-6/n+2=3

Solution for 3n-6/n+2=3 equation:

3n-6/n+2=3

We move all terms to the left:

3n-6/n+2-(3)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

3n-6/n-1=0

We multiply all the terms by the denominator


3n*n-1*n-6=0

We add all the numbers together, and all the variables

-1n+3n*n-6=0

Wy multiply elements

3n^2-1n-6=0

a = 3; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·3·(-6)
Δ = 73
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{-(-1)-\sqrt{73}}{2*3}=\frac{1-\sqrt{73}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{73}}{2*3}=\frac{1+\sqrt{73}}{6}
$