9/4n+3/2n=15/8

Solution for 9/4n+3/2n=15/8 equation:

9/4n+3/2n=15/8

We move all terms to the left:

9/4n+3/2n-(15/8)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

9/4n+3/2n-(+15/8)=0

We get rid of parentheses

9/4n+3/2n-15/8=0

We calculate fractions


(-240n^2)/512n^2+1152n/512n^2+768n/512n^2=0

We multiply all the terms by the denominator


(-240n^2)+1152n+768n=0

We add all the numbers together, and all the variables

(-240n^2)+1920n=0

We get rid of parentheses

-240n^2+1920n=0

a = -240; b = 1920; c = 0;
Δ = b2-4ac
Δ = 19202-4·(-240)·0
Δ = 3686400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3686400}=1920$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1920)-1920}{2*-240}=\frac{-3840}{-480}
=+8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1920)+1920}{2*-240}=\frac{0}{-480}
=0
$