15/8n+17/5n=211/120

Solution for 15/8n+17/5n=211/120 equation:

15/8n+17/5n=211/120

We move all terms to the left:

15/8n+17/5n-(211/120)=0


Domain of the equation: 8n!=0

n!=0/8

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

15/8n+17/5n-(+211/120)=0

We get rid of parentheses

15/8n+17/5n-211/120=0

We calculate fractions


(-42200n^2)/4800n^2+9000n/4800n^2+16320n/4800n^2=0

We multiply all the terms by the denominator


(-42200n^2)+9000n+16320n=0

We add all the numbers together, and all the variables

(-42200n^2)+25320n=0

We get rid of parentheses

-42200n^2+25320n=0

a = -42200; b = 25320; c = 0;
Δ = b2-4ac
Δ = 253202-4·(-42200)·0
Δ = 641102400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{641102400}=25320$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25320)-25320}{2*-42200}=\frac{-50640}{-84400}
=3/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25320)+25320}{2*-42200}=\frac{0}{-84400}
=0
$