0=-15n+10n-0.2n^2

Solution for 0=-15n+10n-0.2n^2 equation:

0=-15n+10n-0.2n^2

We move all terms to the left:

0-(-15n+10n-0.2n^2)=0

We add all the numbers together, and all the variables

-(-15n+10n-0.2n^2)=0

We get rid of parentheses

0.2n^2+15n-10n=0

We add all the numbers together, and all the variables

0.2n^2+5n=0

a = 0.2; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·0.2·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*0.2}=\frac{-10}{0.4}
=-25
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*0.2}=\frac{0}{0.4}
=0
$