(1/4)n=2/5

Solution for (1/4)n=2/5 equation:

(1/4)n=2/5

We move all terms to the left:

(1/4)n-(2/5)=0


Domain of the equation: 4)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+1/4)n-(+2/5)=0

We multiply parentheses

n^2-(+2/5)=0

We get rid of parentheses

n^2-2/5=0

We multiply all the terms by the denominator


n^2*5-2=0

Wy multiply elements

5n^2-2=0

a = 5; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·5·(-2)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10}}{2*5}=\frac{0-2\sqrt{10}}{10}
=-\frac{2\sqrt{10}}{10}
=-\frac{\sqrt{10}}{5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10}}{2*5}=\frac{0+2\sqrt{10}}{10}
=\frac{2\sqrt{10}}{10}
=\frac{\sqrt{10}}{5}
$