-3/2n+1+7/3n=-2/3

Solution for -3/2n+1+7/3n=-2/3 equation:

-3/2n+1+7/3n=-2/3

We move all terms to the left:

-3/2n+1+7/3n-(-2/3)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We get rid of parentheses

-3/2n+7/3n+1+2/3=0

We calculate fractions


(-81n)/54n^2+14n/54n^2+4n/54n^2+1=0

We multiply all the terms by the denominator


(-81n)+14n+4n+1*54n^2=0

We add all the numbers together, and all the variables

18n+(-81n)+1*54n^2=0

Wy multiply elements

54n^2+18n+(-81n)=0

We get rid of parentheses

54n^2+18n-81n=0

We add all the numbers together, and all the variables

54n^2-63n=0

a = 54; b = -63; c = 0;
Δ = b2-4ac
Δ = -632-4·54·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-63}{2*54}=\frac{0}{108}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+63}{2*54}=\frac{126}{108}
=1+1/6
$