0.05n+0.10n(n+8)=2.15

Solution for 0.05n+0.10n(n+8)=2.15 equation:

0.05n+0.10n(n+8)=2.15

We move all terms to the left:

0.05n+0.10n(n+8)-(2.15)=0

We add all the numbers together, and all the variables

0.05n+0.10n(n+8)-2.15=0

We multiply parentheses

0n^2+0.05n+0n-2.15=0

We add all the numbers together, and all the variables

n^2+1.05n-2.15=0

a = 1; b = 1.05; c = -2.15;
Δ = b2-4ac
Δ = 1.052-4·1·(-2.15)
Δ = 9.7025
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{-(1.05)-\sqrt{9.7025}}{2*1}=\frac{-1.05-\sqrt{9.7025}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.05)+\sqrt{9.7025}}{2*1}=\frac{-1.05+\sqrt{9.7025}}{2}
$