n*0.75^(n-1)=3.8

Solution for n*0.75^(n-1)=3.8 equation:

n*0.75^(n-1)=3.8

We move all terms to the left:

n*0.75^(n-1)-(3.8)=0

We add all the numbers together, and all the variables

n*0.75^(n-1)-3.8=0

Wy multiply elements

0n^2-3.8=0

We add all the numbers together, and all the variables

n^2-3.8=0

a = 1; b = 0; c = -3.8;
Δ = b2-4ac
Δ = 02-4·1·(-3.8)
Δ = 15.2
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{-(0)-\sqrt{15.2}}{2*1}=\frac{0-\sqrt{15.2}}{2}
=-\frac{\sqrt{}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{15.2}}{2*1}=\frac{0+\sqrt{15.2}}{2}
=\frac{\sqrt{}}{2}
$