1/2n+7=14n+2n

Solution for 1/2n+7=14n+2n equation:

1/2n+7=14n+2n

We move all terms to the left:

1/2n+7-(14n+2n)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

1/2n-(+16n)+7=0

We get rid of parentheses

1/2n-16n+7=0

We multiply all the terms by the denominator


-16n*2n+7*2n+1=0

Wy multiply elements

-32n^2+14n+1=0

a = -32; b = 14; c = +1;
Δ = b2-4ac
Δ = 142-4·(-32)·1
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-18}{2*-32}=\frac{-32}{-64}
=1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+18}{2*-32}=\frac{4}{-64}
=-1/16
$