1/4n+18=n

Solution for 1/4n+18=n equation:

1/4n+18=n

We move all terms to the left:

1/4n+18-(n)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We add all the numbers together, and all the variables

-1n+1/4n+18=0

We multiply all the terms by the denominator


-1n*4n+18*4n+1=0

Wy multiply elements

-4n^2+72n+1=0

a = -4; b = 72; c = +1;
Δ = b2-4ac
Δ = 722-4·(-4)·1
Δ = 5200
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:

$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-20\sqrt{13}}{2*-4}=\frac{-72-20\sqrt{13}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+20\sqrt{13}}{2*-4}=\frac{-72+20\sqrt{13}}{-8}
$