1/4n+3/28n+11/4=3/2

Solution for 1/4n+3/28n+11/4=3/2 equation:

1/4n+3/28n+11/4=3/2

We move all terms to the left:

1/4n+3/28n+11/4-(3/2)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 28n!=0

n!=0/28

n!=0

n∈R


We add all the numbers together, and all the variables

1/4n+3/28n+11/4-(+3/2)=0

We get rid of parentheses

1/4n+3/28n+11/4-3/2=0

We calculate fractions


(-2688n^2)/3584n^2+112n/3584n^2+384n/3584n^2+1232n/3584n^2=0

We multiply all the terms by the denominator


(-2688n^2)+112n+384n+1232n=0

We add all the numbers together, and all the variables

(-2688n^2)+1728n=0

We get rid of parentheses

-2688n^2+1728n=0

a = -2688; b = 1728; c = 0;
Δ = b2-4ac
Δ = 17282-4·(-2688)·0
Δ = 2985984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2985984}=1728$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1728)-1728}{2*-2688}=\frac{-3456}{-5376}
=9/14
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1728)+1728}{2*-2688}=\frac{0}{-5376}
=0
$