1/2n=-12-2/3n

Solution for 1/2n=-12-2/3n equation:

1/2n=-12-2/3n

We move all terms to the left:

1/2n-(-12-2/3n)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 3n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

1/2n-(-2/3n-12)=0

We get rid of parentheses

1/2n+2/3n+12=0

We calculate fractions


3n/6n^2+4n/6n^2+12=0

We multiply all the terms by the denominator


3n+4n+12*6n^2=0

We add all the numbers together, and all the variables

7n+12*6n^2=0

Wy multiply elements

72n^2+7n=0

a = 72; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·72·0
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*72}=\frac{-14}{144}
=-7/72
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*72}=\frac{0}{144}
=0
$