5/4n-9/5=1/8n

Solution for 5/4n-9/5=1/8n equation:

5/4n-9/5=1/8n

We move all terms to the left:

5/4n-9/5-(1/8n)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 8n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

5/4n-(+1/8n)-9/5=0

We get rid of parentheses

5/4n-1/8n-9/5=0

We calculate fractions


(-2304n^2)/800n^2+1000n/800n^2+(-100n)/800n^2=0

We multiply all the terms by the denominator


(-2304n^2)+1000n+(-100n)=0

We get rid of parentheses

-2304n^2+1000n-100n=0

We add all the numbers together, and all the variables

-2304n^2+900n=0

a = -2304; b = 900; c = 0;
Δ = b2-4ac
Δ = 9002-4·(-2304)·0
Δ = 810000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{810000}=900$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(900)-900}{2*-2304}=\frac{-1800}{-4608}
=25/64
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(900)+900}{2*-2304}=\frac{0}{-4608}
=0
$