2/3n-1/2n=7+3/4

Solution for 2/3n-1/2n=7+3/4 equation:

2/3n-1/2n=7+3/4

We move all terms to the left:

2/3n-1/2n-(7+3/4)=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 add all the numbers together, and all the variables

2/3n-1/2n-(3/4+7)=0

We get rid of parentheses

2/3n-1/2n-7-3/4=0

We calculate fractions


(-36n^2)/96n^2+64n/96n^2+(-48n)/96n^2-7=0

We multiply all the terms by the denominator


(-36n^2)+64n+(-48n)-7*96n^2=0

Wy multiply elements

(-36n^2)-672n^2+64n+(-48n)=0

We get rid of parentheses

-36n^2-672n^2+64n-48n=0

We add all the numbers together, and all the variables

-708n^2+16n=0

a = -708; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-708)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-708}=\frac{-32}{-1416}
=4/177
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-708}=\frac{0}{-1416}
=0
$