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!=0/3

n!=0

n∈R


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^2-126n+5=0

a = -9; b = -126; c = +5;
Δ = b2-4ac
Δ = -1262-4·(-9)·5
Δ = 16056
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:

$\sqrt{\Delta}=\sqrt{16056}=\sqrt{36*446}=\sqrt{36}*\sqrt{446}=6\sqrt{446}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-6\sqrt{446}}{2*-9}=\frac{126-6\sqrt{446}}{-18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+6\sqrt{446}}{2*-9}=\frac{126+6\sqrt{446}}{-18}
$