7-2/3n=1/2n+5

Solution for 7-2/3n=1/2n+5 equation:

7-2/3n=1/2n+5

We move all terms to the left:

7-2/3n-(1/2n+5)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 2n+5)!=0

n∈R


We get rid of parentheses

-2/3n-1/2n-5+7=0

We calculate fractions


(-4n)/6n^2+(-3n)/6n^2-5+7=0

We add all the numbers together, and all the variables

(-4n)/6n^2+(-3n)/6n^2+2=0

We multiply all the terms by the denominator


(-4n)+(-3n)+2*6n^2=0

Wy multiply elements

12n^2+(-4n)+(-3n)=0

We get rid of parentheses

12n^2-4n-3n=0

We add all the numbers together, and all the variables

12n^2-7n=0

a = 12; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·12·0
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*12}=\frac{0}{24}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*12}=\frac{14}{24}
=7/12
$