17/3n-2=17/2n-14

Solution for 17/3n-2=17/2n-14 equation:

17/3n-2=17/2n-14

We move all terms to the left:

17/3n-2-(17/2n-14)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 2n-14)!=0

n∈R


We get rid of parentheses

17/3n-17/2n+14-2=0

We calculate fractions


34n/6n^2+(-51n)/6n^2+14-2=0

We add all the numbers together, and all the variables

34n/6n^2+(-51n)/6n^2+12=0

We multiply all the terms by the denominator


34n+(-51n)+12*6n^2=0

Wy multiply elements

72n^2+34n+(-51n)=0

We get rid of parentheses

72n^2+34n-51n=0

We add all the numbers together, and all the variables

72n^2-17n=0

a = 72; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·72·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*72}=\frac{0}{144}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*72}=\frac{34}{144}
=17/72
$