1/3n+25=2n

Solution for 1/3n+25=2n equation:

1/3n+25=2n

We move all terms to the left:

1/3n+25-(2n)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

-2n+1/3n+25=0

We multiply all the terms by the denominator


-2n*3n+25*3n+1=0

Wy multiply elements

-6n^2+75n+1=0

a = -6; b = 75; c = +1;
Δ = b2-4ac
Δ = 752-4·(-6)·1
Δ = 5649
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{-(75)-\sqrt{5649}}{2*-6}=\frac{-75-\sqrt{5649}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+\sqrt{5649}}{2*-6}=\frac{-75+\sqrt{5649}}{-12}
$