5/4n-2/5n-13=21

Solution for 5/4n-2/5n-13=21 equation:

5/4n-2/5n-13=21

We move all terms to the left:

5/4n-2/5n-13-(21)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We add all the numbers together, and all the variables

5/4n-2/5n-34=0

We calculate fractions


25n/20n^2+(-8n)/20n^2-34=0

We multiply all the terms by the denominator


25n+(-8n)-34*20n^2=0

Wy multiply elements

-680n^2+25n+(-8n)=0

We get rid of parentheses

-680n^2+25n-8n=0

We add all the numbers together, and all the variables

-680n^2+17n=0

a = -680; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-680)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-680}=\frac{-34}{-1360}
=1/40
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-680}=\frac{0}{-1360}
=0
$