2-0.1/2n=3n+16

Solution for 2-0.1/2n=3n+16 equation:

2-0.1/2n=3n+16

We move all terms to the left:

2-0.1/2n-(3n+16)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We get rid of parentheses

-0.1/2n-3n-16+2=0

We multiply all the terms by the denominator


-3n*2n-16*2n+2*2n-0.1=0

Wy multiply elements

-6n^2-32n+4n-0.1=0

We add all the numbers together, and all the variables

-6n^2-28n-0.1=0

a = -6; b = -28; c = -0.1;
Δ = b2-4ac
Δ = -282-4·(-6)·(-0.1)
Δ = 781.6
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-\sqrt{781.6}}{2*-6}=\frac{28-\sqrt{781.6}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+\sqrt{781.6}}{2*-6}=\frac{28+\sqrt{781.6}}{-12}
$