n-1/2n=17

Solution for n-1/2n=17 equation:

n-1/2n=17

We move all terms to the left:

n-1/2n-(17)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We multiply all the terms by the denominator


n*2n-17*2n-1=0

Wy multiply elements

2n^2-34n-1=0

a = 2; b = -34; c = -1;
Δ = b2-4ac
Δ = -342-4·2·(-1)
Δ = 1164
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:

$\sqrt{\Delta}=\sqrt{1164}=\sqrt{4*291}=\sqrt{4}*\sqrt{291}=2\sqrt{291}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{291}}{2*2}=\frac{34-2\sqrt{291}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{291}}{2*2}=\frac{34+2\sqrt{291}}{4}
$