2n+2/n=10

Solution for 2n+2/n=10 equation:

2n+2/n=10

We move all terms to the left:

2n+2/n-(10)=0


Domain of the equation: n!=0

n∈R


We multiply all the terms by the denominator


2n*n-10*n+2=0

We add all the numbers together, and all the variables

-10n+2n*n+2=0

Wy multiply elements

2n^2-10n+2=0

a = 2; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·2·2
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{21}}{2*2}=\frac{10-2\sqrt{21}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{21}}{2*2}=\frac{10+2\sqrt{21}}{4}
$