11/16n-3+1/4n=2/4

Solution for 11/16n-3+1/4n=2/4 equation:

11/16n-3+1/4n=2/4

We move all terms to the left:

11/16n-3+1/4n-(2/4)=0


Domain of the equation: 16n!=0

n!=0/16

n!=0

n∈R



Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We add all the numbers together, and all the variables

11/16n+1/4n-3-(+2/4)=0

We get rid of parentheses

11/16n+1/4n-3-2/4=0

We calculate fractions


704n/1024n^2+16n/1024n^2+(-32n)/1024n^2-3=0

We multiply all the terms by the denominator


704n+16n+(-32n)-3*1024n^2=0

We add all the numbers together, and all the variables

720n+(-32n)-3*1024n^2=0

Wy multiply elements

-3072n^2+720n+(-32n)=0

We get rid of parentheses

-3072n^2+720n-32n=0

We add all the numbers together, and all the variables

-3072n^2+688n=0

a = -3072; b = 688; c = 0;
Δ = b2-4ac
Δ = 6882-4·(-3072)·0
Δ = 473344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{473344}=688$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(688)-688}{2*-3072}=\frac{-1376}{-6144}
=43/192
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(688)+688}{2*-3072}=\frac{0}{-6144}
=0
$