0=0.4n^2+0.6n-378

Solution for 0=0.4n^2+0.6n-378 equation:

0=0.4n^2+0.6n-378

We move all terms to the left:

0-(0.4n^2+0.6n-378)=0

We add all the numbers together, and all the variables

-(0.4n^2+0.6n-378)=0

We get rid of parentheses

-0.4n^2-0.6n+378=0

a = -0.4; b = -0.6; c = +378;
Δ = b2-4ac
Δ = -0.62-4·(-0.4)·378
Δ = 605.16
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{-(-0.6)-\sqrt{605.16}}{2*-0.4}=\frac{0.6-\sqrt{605.16}}{-0.8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.6)+\sqrt{605.16}}{2*-0.4}=\frac{0.6+\sqrt{605.16}}{-0.8}
$