7/4n+1/3n=25/6

Solution for 7/4n+1/3n=25/6 equation:

7/4n+1/3n=25/6

We move all terms to the left:

7/4n+1/3n-(25/6)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

7/4n+1/3n-(+25/6)=0

We get rid of parentheses

7/4n+1/3n-25/6=0

We calculate fractions


(-900n^2)/432n^2+756n/432n^2+144n/432n^2=0

We multiply all the terms by the denominator


(-900n^2)+756n+144n=0

We add all the numbers together, and all the variables

(-900n^2)+900n=0

We get rid of parentheses

-900n^2+900n=0

a = -900; b = 900; c = 0;
Δ = b2-4ac
Δ = 9002-4·(-900)·0
Δ = 810000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{810000}=900$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(900)-900}{2*-900}=\frac{-1800}{-1800}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(900)+900}{2*-900}=\frac{0}{-1800}
=0
$