1/7n-n=18

Solution for 1/7n-n=18 equation:

1/7n-n=18

We move all terms to the left:

1/7n-n-(18)=0


Domain of the equation: 7n!=0

n!=0/7

n!=0

n∈R


We add all the numbers together, and all the variables

-1n+1/7n-18=0

We multiply all the terms by the denominator


-1n*7n-18*7n+1=0

Wy multiply elements

-7n^2-126n+1=0

a = -7; b = -126; c = +1;
Δ = b2-4ac
Δ = -1262-4·(-7)·1
Δ = 15904
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:

$\sqrt{\Delta}=\sqrt{15904}=\sqrt{16*994}=\sqrt{16}*\sqrt{994}=4\sqrt{994}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-4\sqrt{994}}{2*-7}=\frac{126-4\sqrt{994}}{-14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+4\sqrt{994}}{2*-7}=\frac{126+4\sqrt{994}}{-14}
$