1/2n+n=15

Solution for 1/2n+n=15 equation:

1/2n+n=15

We move all terms to the left:

1/2n+n-(15)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

n+1/2n-15=0

We multiply all the terms by the denominator


n*2n-15*2n+1=0

Wy multiply elements

2n^2-30n+1=0

a = 2; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·2·1
Δ = 892
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:

$\sqrt{\Delta}=\sqrt{892}=\sqrt{4*223}=\sqrt{4}*\sqrt{223}=2\sqrt{223}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{223}}{2*2}=\frac{30-2\sqrt{223}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{223}}{2*2}=\frac{30+2\sqrt{223}}{4}
$