9/8n+5/4n=-133/16

Solution for 9/8n+5/4n=-133/16 equation:

9/8n+5/4n=-133/16

We move all terms to the left:

9/8n+5/4n-(-133/16)=0


Domain of the equation: 8n!=0

n!=0/8

n!=0

n∈R



Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We get rid of parentheses

9/8n+5/4n+133/16=0

We calculate fractions


17024n^2/512n^2+576n/512n^2+640n/512n^2=0

We multiply all the terms by the denominator


17024n^2+576n+640n=0

We add all the numbers together, and all the variables

17024n^2+1216n=0

a = 17024; b = 1216; c = 0;
Δ = b2-4ac
Δ = 12162-4·17024·0
Δ = 1478656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1478656}=1216$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1216)-1216}{2*17024}=\frac{-2432}{34048}
=-1/14
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1216)+1216}{2*17024}=\frac{0}{34048}
=0
$