(15/n-1)(n-1)=59

Solution for (15/n-1)(n-1)=59 equation:

(15/n-1)(n-1)=59

We move all terms to the left:

(15/n-1)(n-1)-(59)=0


Domain of the equation: n-1)(n-1)!=0

n∈R


We multiply parentheses ..

(+15n^2-15n-1n+1)-59=0

We get rid of parentheses

15n^2-15n-1n+1-59=0

We add all the numbers together, and all the variables

15n^2-16n-58=0

a = 15; b = -16; c = -58;
Δ = b2-4ac
Δ = -162-4·15·(-58)
Δ = 3736
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:

$\sqrt{\Delta}=\sqrt{3736}=\sqrt{4*934}=\sqrt{4}*\sqrt{934}=2\sqrt{934}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{934}}{2*15}=\frac{16-2\sqrt{934}}{30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{934}}{2*15}=\frac{16+2\sqrt{934}}{30}
$