7/4n+38/15=-1/6n+1

Solution for 7/4n+38/15=-1/6n+1 equation:

7/4n+38/15=-1/6n+1

We move all terms to the left:

7/4n+38/15-(-1/6n+1)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 6n+1)!=0

n∈R


We get rid of parentheses

7/4n+1/6n-1+38/15=0

We calculate fractions


5472n^2/360n^2+630n/360n^2+60n/360n^2-1=0

We multiply all the terms by the denominator


5472n^2+630n+60n-1*360n^2=0

We add all the numbers together, and all the variables

5472n^2+690n-1*360n^2=0

Wy multiply elements

5472n^2-360n^2+690n=0

We add all the numbers together, and all the variables

5112n^2+690n=0

a = 5112; b = 690; c = 0;
Δ = b2-4ac
Δ = 6902-4·5112·0
Δ = 476100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{476100}=690$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(690)-690}{2*5112}=\frac{-1380}{10224}
=-115/852
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(690)+690}{2*5112}=\frac{0}{10224}
=0
$