n+2/7n=81

Solution for n+2/7n=81 equation:

n+2/7n=81

We move all terms to the left:

n+2/7n-(81)=0


Domain of the equation: 7n!=0

n!=0/7

n!=0

n∈R


We multiply all the terms by the denominator


n*7n-81*7n+2=0

Wy multiply elements

7n^2-567n+2=0

a = 7; b = -567; c = +2;
Δ = b2-4ac
Δ = -5672-4·7·2
Δ = 321433
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-567)-\sqrt{321433}}{2*7}=\frac{567-\sqrt{321433}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-567)+\sqrt{321433}}{2*7}=\frac{567+\sqrt{321433}}{14}
$