1/3n-1716=3n

Solution for 1/3n-1716=3n equation:

1/3n-1716=3n

We move all terms to the left:

1/3n-1716-(3n)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

-3n+1/3n-1716=0

We multiply all the terms by the denominator


-3n*3n-1716*3n+1=0

Wy multiply elements

-9n^2-5148n+1=0

a = -9; b = -5148; c = +1;
Δ = b2-4ac
Δ = -51482-4·(-9)·1
Δ = 26501940
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:

$\sqrt{\Delta}=\sqrt{26501940}=\sqrt{36*736165}=\sqrt{36}*\sqrt{736165}=6\sqrt{736165}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5148)-6\sqrt{736165}}{2*-9}=\frac{5148-6\sqrt{736165}}{-18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5148)+6\sqrt{736165}}{2*-9}=\frac{5148+6\sqrt{736165}}{-18}
$