n-5/2n=60

Solution for n-5/2n=60 equation:

n-5/2n=60

We move all terms to the left:

n-5/2n-(60)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We multiply all the terms by the denominator


n*2n-60*2n-5=0

Wy multiply elements

2n^2-120n-5=0

a = 2; b = -120; c = -5;
Δ = b2-4ac
Δ = -1202-4·2·(-5)
Δ = 14440
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:

$\sqrt{\Delta}=\sqrt{14440}=\sqrt{1444*10}=\sqrt{1444}*\sqrt{10}=38\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-38\sqrt{10}}{2*2}=\frac{120-38\sqrt{10}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+38\sqrt{10}}{2*2}=\frac{120+38\sqrt{10}}{4}
$