0.05n+0.10n(n+9)=2.85

Solution for 0.05n+0.10n(n+9)=2.85 equation:

0.05n+0.10n(n+9)=2.85

We move all terms to the left:

0.05n+0.10n(n+9)-(2.85)=0

We add all the numbers together, and all the variables

0.05n+0.10n(n+9)-2.85=0

We multiply parentheses

0n^2+0.05n+0n-2.85=0

We add all the numbers together, and all the variables

n^2+1.05n-2.85=0

a = 1; b = 1.05; c = -2.85;
Δ = b2-4ac
Δ = 1.052-4·1·(-2.85)
Δ = 12.5025
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{12.5025}}{2*1}=\frac{-1.05-\sqrt{12.5025}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.05)+\sqrt{12.5025}}{2*1}=\frac{-1.05+\sqrt{12.5025}}{2}
$