9+4n=1/2n-1

Solution for 9+4n=1/2n-1 equation:

9+4n=1/2n-1

We move all terms to the left:

9+4n-(1/2n-1)=0


Domain of the equation: 2n-1)!=0

n∈R


We get rid of parentheses

4n-1/2n+1+9=0

We multiply all the terms by the denominator


4n*2n+1*2n+9*2n-1=0

Wy multiply elements

8n^2+2n+18n-1=0

We add all the numbers together, and all the variables

8n^2+20n-1=0

a = 8; b = 20; c = -1;
Δ = b2-4ac
Δ = 202-4·8·(-1)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-12\sqrt{3}}{2*8}=\frac{-20-12\sqrt{3}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+12\sqrt{3}}{2*8}=\frac{-20+12\sqrt{3}}{16}
$