n=3,4n-6/n+2=

Solution for n=3,4n-6/n+2= equation:

n=3.4n-6/n+2=

We move all terms to the left:

n-(3.4n-6/n+2)=0


Domain of the equation: n+2)!=0

n∈R


We get rid of parentheses

n-3.4n+6/n-2=0

We multiply all the terms by the denominator


n*n-(3.4n)*n-2*n+6=0

We add all the numbers together, and all the variables

n*n-(+3.4n)*n-2*n+6=0

We add all the numbers together, and all the variables

-2n+n*n-(+3.4n)*n+6=0

We multiply parentheses

-3n^2-2n+n*n+6=0

Wy multiply elements

-3n^2+n^2-2n+6=0

We add all the numbers together, and all the variables

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

a = -2; b = -2; c = +6;
Δ = b2-4ac
Δ = -22-4·(-2)·6
Δ = 52
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{13}}{2*-2}=\frac{2-2\sqrt{13}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{13}}{2*-2}=\frac{2+2\sqrt{13}}{-4}
$