1/4n-15=2n-1

Solution for 1/4n-15=2n-1 equation:

1/4n-15=2n-1

We move all terms to the left:

1/4n-15-(2n-1)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We get rid of parentheses

1/4n-2n+1-15=0

We multiply all the terms by the denominator


-2n*4n+1*4n-15*4n+1=0

Wy multiply elements

-8n^2+4n-60n+1=0

We add all the numbers together, and all the variables

-8n^2-56n+1=0

a = -8; b = -56; c = +1;
Δ = b2-4ac
Δ = -562-4·(-8)·1
Δ = 3168
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:

$\sqrt{\Delta}=\sqrt{3168}=\sqrt{144*22}=\sqrt{144}*\sqrt{22}=12\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-12\sqrt{22}}{2*-8}=\frac{56-12\sqrt{22}}{-16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+12\sqrt{22}}{2*-8}=\frac{56+12\sqrt{22}}{-16}
$