-3n-6=1/2n

Solution for -3n-6=1/2n equation:

-3n-6=1/2n

We move all terms to the left:

-3n-6-(1/2n)=0


Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

-3n-(+1/2n)-6=0

We get rid of parentheses

-3n-1/2n-6=0

We multiply all the terms by the denominator


-3n*2n-6*2n-1=0

Wy multiply elements

-6n^2-12n-1=0

a = -6; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·(-6)·(-1)
Δ = 120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{30}}{2*-6}=\frac{12-2\sqrt{30}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{30}}{2*-6}=\frac{12+2\sqrt{30}}{-12}
$