n+2/n=72

Solution for n+2/n=72 equation:

n+2/n=72

We move all terms to the left:

n+2/n-(72)=0


Domain of the equation: n!=0

n∈R


We multiply all the terms by the denominator


n*n-72*n+2=0

We add all the numbers together, and all the variables

-72n+n*n+2=0

Wy multiply elements

n^2-72n+2=0

a = 1; b = -72; c = +2;
Δ = b2-4ac
Δ = -722-4·1·2
Δ = 5176
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:

$\sqrt{\Delta}=\sqrt{5176}=\sqrt{4*1294}=\sqrt{4}*\sqrt{1294}=2\sqrt{1294}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1294}}{2*1}=\frac{72-2\sqrt{1294}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1294}}{2*1}=\frac{72+2\sqrt{1294}}{2}
$