3n-5/n=14

Solution for 3n-5/n=14 equation:

3n-5/n=14

We move all terms to the left:

3n-5/n-(14)=0


Domain of the equation: n!=0

n∈R


We multiply all the terms by the denominator


3n*n-14*n-5=0

We add all the numbers together, and all the variables

-14n+3n*n-5=0

Wy multiply elements

3n^2-14n-5=0

a = 3; b = -14; c = -5;
Δ = b2-4ac
Δ = -142-4·3·(-5)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-16}{2*3}=\frac{-2}{6}
=-1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+16}{2*3}=\frac{30}{6}
=5
$