7/3n-7/2n=-7/4

Solution for 7/3n-7/2n=-7/4 equation:

7/3n-7/2n=-7/4

We move all terms to the left:

7/3n-7/2n-(-7/4)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We get rid of parentheses

7/3n-7/2n+7/4=0

We calculate fractions


84n^2/96n^2+224n/96n^2+(-336n)/96n^2=0

We multiply all the terms by the denominator


84n^2+224n+(-336n)=0

We get rid of parentheses

84n^2+224n-336n=0

We add all the numbers together, and all the variables

84n^2-112n=0

a = 84; b = -112; c = 0;
Δ = b2-4ac
Δ = -1122-4·84·0
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-112}{2*84}=\frac{0}{168}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+112}{2*84}=\frac{224}{168}
=1+1/3
$