0.1=x*0.05*0.95^(x-1)

Solution for 0.1=x*0.05*0.95^(x-1) equation:

0.1=x*0.05*0.95^(x-1)

We move all terms to the left:

0.1-(x*0.05*0.95^(x-1))=0


We calculate terms in parentheses: -(x*0.05*0.95^(x-1)), so:

x*0.05*0.95^(x-1)

Wy multiply elements

0x^2

We add all the numbers together, and all the variables

x^2

Back to the equation:

-(x^2)


We add all the numbers together, and all the variables

-1x^2+0.1=0

a = -1; b = 0; c = +0.1;
Δ = b2-4ac
Δ = 02-4·(-1)·0.1
Δ = 0.4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-\sqrt{0.4}}{2*-1}=\frac{0-\sqrt{0.4}}{-2}
=-\frac{\sqrt{}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{0.4}}{2*-1}=\frac{0+\sqrt{0.4}}{-2}
=\frac{\sqrt{}}{-2}
$