14/2n+n=38

Solution for 14/2n+n=38 equation:

14/2n+n=38

We move all terms to the left:

14/2n+n-(38)=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+14/2n-38=0

We multiply all the terms by the denominator


n*2n-38*2n+14=0

Wy multiply elements

2n^2-76n+14=0

a = 2; b = -76; c = +14;
Δ = b2-4ac
Δ = -762-4·2·14
Δ = 5664
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:

$\sqrt{\Delta}=\sqrt{5664}=\sqrt{16*354}=\sqrt{16}*\sqrt{354}=4\sqrt{354}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-4\sqrt{354}}{2*2}=\frac{76-4\sqrt{354}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+4\sqrt{354}}{2*2}=\frac{76+4\sqrt{354}}{4}
$