-3/2n+5/4n=-1/5

Solution for -3/2n+5/4n=-1/5 equation:

-3/2n+5/4n=-1/5

We move all terms to the left:

-3/2n+5/4n-(-1/5)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We get rid of parentheses

-3/2n+5/4n+1/5=0

We calculate fractions


32n^2/200n^2+(-300n)/200n^2+250n/200n^2=0

We multiply all the terms by the denominator


32n^2+(-300n)+250n=0

We add all the numbers together, and all the variables

32n^2+250n+(-300n)=0

We get rid of parentheses

32n^2+250n-300n=0

We add all the numbers together, and all the variables

32n^2-50n=0

a = 32; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·32·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*32}=\frac{0}{64}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*32}=\frac{100}{64}
=1+9/16
$