(5/3n)-17=3n-25

Solution for (5/3n)-17=3n-25 equation:

(5/3n)-17=3n-25

We move all terms to the left:

(5/3n)-17-(3n-25)=0


Domain of the equation: 3n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+5/3n)-(3n-25)-17=0

We get rid of parentheses

5/3n-3n+25-17=0

We multiply all the terms by the denominator


-3n*3n+25*3n-17*3n+5=0

Wy multiply elements

-9n^2+75n-51n+5=0

We add all the numbers together, and all the variables

-9n^2+24n+5=0

a = -9; b = 24; c = +5;
Δ = b2-4ac
Δ = 242-4·(-9)·5
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{21}}{2*-9}=\frac{-24-6\sqrt{21}}{-18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{21}}{2*-9}=\frac{-24+6\sqrt{21}}{-18}
$