10=2n+1/2n

Solution for 10=2n+1/2n equation:

10=2n+1/2n

We move all terms to the left:

10-(2n+1/2n)=0


Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

-(+2n+1/2n)+10=0

We get rid of parentheses

-2n-1/2n+10=0

We multiply all the terms by the denominator


-2n*2n+10*2n-1=0

Wy multiply elements

-4n^2+20n-1=0

a = -4; b = 20; c = -1;
Δ = b2-4ac
Δ = 202-4·(-4)·(-1)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-8\sqrt{6}}{2*-4}=\frac{-20-8\sqrt{6}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8\sqrt{6}}{2*-4}=\frac{-20+8\sqrt{6}}{-8}
$