2/3n+1/2n=7

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

2/3n+1/2n=7

We move all terms to the left:

2/3n+1/2n-(7)=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 calculate fractions


4n/6n^2+3n/6n^2-7=0

We multiply all the terms by the denominator


4n+3n-7*6n^2=0

We add all the numbers together, and all the variables

7n-7*6n^2=0

Wy multiply elements

-42n^2+7n=0

a = -42; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-42)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-42}=\frac{-14}{-84}
=1/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-42}=\frac{0}{-84}
=0
$