1/2n=18+5n

Solution for 1/2n=18+5n equation:

1/2n=18+5n

We move all terms to the left:

1/2n-(18+5n)=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-(5n+18)=0

We get rid of parentheses

1/2n-5n-18=0

We multiply all the terms by the denominator


-5n*2n-18*2n+1=0

Wy multiply elements

-10n^2-36n+1=0

a = -10; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·(-10)·1
Δ = 1336
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:

$\sqrt{\Delta}=\sqrt{1336}=\sqrt{4*334}=\sqrt{4}*\sqrt{334}=2\sqrt{334}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{334}}{2*-10}=\frac{36-2\sqrt{334}}{-20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{334}}{2*-10}=\frac{36+2\sqrt{334}}{-20}
$