13/14n+4/7n-1/28=7/4

Solution for 13/14n+4/7n-1/28=7/4 equation:

13/14n+4/7n-1/28=7/4

We move all terms to the left:

13/14n+4/7n-1/28-(7/4)=0


Domain of the equation: 14n!=0

n!=0/14

n!=0

n∈R



Domain of the equation: 7n!=0

n!=0/7

n!=0

n∈R


We add all the numbers together, and all the variables

13/14n+4/7n-1/28-(+7/4)=0

We get rid of parentheses

13/14n+4/7n-1/28-7/4=0

We calculate fractions


(-2744n^2)/21952n^2+(-134456n^2)/21952n^2+20384n/21952n^2+12544n/21952n^2=0

We multiply all the terms by the denominator


(-2744n^2)+(-134456n^2)+20384n+12544n=0

We add all the numbers together, and all the variables

(-2744n^2)+(-134456n^2)+32928n=0

We get rid of parentheses

-2744n^2-134456n^2+32928n=0

We add all the numbers together, and all the variables

-137200n^2+32928n=0

a = -137200; b = 32928; c = 0;
Δ = b2-4ac
Δ = 329282-4·(-137200)·0
Δ = 1084253184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1084253184}=32928$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32928)-32928}{2*-137200}=\frac{-65856}{-274400}
=6/25
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32928)+32928}{2*-137200}=\frac{0}{-274400}
=0
$