2/3n=5n-39

Solution for 2/3n=5n-39 equation:

2/3n=5n-39

We move all terms to the left:

2/3n-(5n-39)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We get rid of parentheses

2/3n-5n+39=0

We multiply all the terms by the denominator


-5n*3n+39*3n+2=0

Wy multiply elements

-15n^2+117n+2=0

a = -15; b = 117; c = +2;
Δ = b2-4ac
Δ = 1172-4·(-15)·2
Δ = 13809
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{-(117)-\sqrt{13809}}{2*-15}=\frac{-117-\sqrt{13809}}{-30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(117)+\sqrt{13809}}{2*-15}=\frac{-117+\sqrt{13809}}{-30}
$