1,2n=0,5+1/5n

Solution for 1,2n=0,5+1/5n equation:

1.2n=0.5+1/5n

We move all terms to the left:

1.2n-(0.5+1/5n)=0


Domain of the equation: 5n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

1.2n-(1/5n+0.5)=0

We get rid of parentheses

1.2n-1/5n-0.5=0

We multiply all the terms by the denominator


(1.2n)*5n-(0.5)*5n-1=0

We add all the numbers together, and all the variables

(+1.2n)*5n-(0.5)*5n-1=0

We multiply parentheses

5n^2-2.5n-1=0

a = 5; b = -2.5; c = -1;
Δ = b2-4ac
Δ = -2.52-4·5·(-1)
Δ = 26.25
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{-(-2.5)-\sqrt{26.25}}{2*5}=\frac{2.5-\sqrt{26.25}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.5)+\sqrt{26.25}}{2*5}=\frac{2.5+\sqrt{26.25}}{10}
$