1/n+17=12n-8

Solution for 1/n+17=12n-8 equation:

1/n+17=12n-8

We move all terms to the left:

1/n+17-(12n-8)=0


Domain of the equation: n!=0

n∈R


We get rid of parentheses

1/n-12n+8+17=0

We multiply all the terms by the denominator


-12n*n+8*n+17*n+1=0

We add all the numbers together, and all the variables

25n-12n*n+1=0

Wy multiply elements

-12n^2+25n+1=0

a = -12; b = 25; c = +1;
Δ = b2-4ac
Δ = 252-4·(-12)·1
Δ = 673
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-\sqrt{673}}{2*-12}=\frac{-25-\sqrt{673}}{-24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{673}}{2*-12}=\frac{-25+\sqrt{673}}{-24}
$