n-1/5n=15

Solution for n-1/5n=15 equation:

n-1/5n=15

We move all terms to the left:

n-1/5n-(15)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We multiply all the terms by the denominator


n*5n-15*5n-1=0

Wy multiply elements

5n^2-75n-1=0

a = 5; b = -75; c = -1;
Δ = b2-4ac
Δ = -752-4·5·(-1)
Δ = 5645
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{-(-75)-\sqrt{5645}}{2*5}=\frac{75-\sqrt{5645}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{5645}}{2*5}=\frac{75+\sqrt{5645}}{10}
$