.25n+10n=2/3n

Solution for .25n+10n=2/3n equation:

.25n+10n=2/3n

We move all terms to the left:

.25n+10n-(2/3n)=0


Domain of the equation: 3n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

.25n+10n-(+2/3n)=0

We add all the numbers together, and all the variables

10.25n-(+2/3n)=0

We get rid of parentheses

10.25n-2/3n=0

We multiply all the terms by the denominator


(10.25n)*3n-2=0

We add all the numbers together, and all the variables

(+10.25n)*3n-2=0

We multiply parentheses

30n^2-2=0

a = 30; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·30·(-2)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*30}=\frac{0-4\sqrt{15}}{60}
=-\frac{4\sqrt{15}}{60}
=-\frac{\sqrt{15}}{15}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*30}=\frac{0+4\sqrt{15}}{60}
=\frac{4\sqrt{15}}{60}
=\frac{\sqrt{15}}{15}
$