2/3n+1/6n=25

Solution for 2/3n+1/6n=25 equation:

2/3n+1/6n=25

We move all terms to the left:

2/3n+1/6n-(25)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R


We calculate fractions


12n/18n^2+3n/18n^2-25=0

We multiply all the terms by the denominator


12n+3n-25*18n^2=0

We add all the numbers together, and all the variables

15n-25*18n^2=0

Wy multiply elements

-450n^2+15n=0

a = -450; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-450)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-450}=\frac{-30}{-900}
=1/30
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-450}=\frac{0}{-900}
=0
$