4/2=n+8/n-6

Solution for 4/2=n+8/n-6 equation:

4/2=n+8/n-6

We move all terms to the left:

4/2-(n+8/n-6)=0


Domain of the equation: n-6)!=0

n∈R


We add all the numbers together, and all the variables

-(n+8/n-6)+2=0

We get rid of parentheses

-n-8/n+6+2=0

We multiply all the terms by the denominator


-n*n+6*n+2*n-8=0

We add all the numbers together, and all the variables

8n-n*n-8=0

Wy multiply elements

-1n^2+8n-8=0

a = -1; b = 8; c = -8;
Δ = b2-4ac
Δ = 82-4·(-1)·(-8)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{2}}{2*-1}=\frac{-8-4\sqrt{2}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{2}}{2*-1}=\frac{-8+4\sqrt{2}}{-2}
$