n(-5/8)=-0.4

Solution for n(-5/8)=-0.4 equation:

n(-5/8)=-0.4

We move all terms to the left:

n(-5/8)-(-0.4)=0

We add all the numbers together, and all the variables

n(-5/8)+0.4=0

We multiply parentheses

-5n^2+0.4=0

a = -5; b = 0; c = +0.4;
Δ = b2-4ac
Δ = 02-4·(-5)·0.4
Δ = 8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2}}{2*-5}=\frac{0-2\sqrt{2}}{-10}
=-\frac{2\sqrt{2}}{-10}
=-\frac{\sqrt{2}}{-5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2}}{2*-5}=\frac{0+2\sqrt{2}}{-10}
=\frac{2\sqrt{2}}{-10}
=\frac{\sqrt{2}}{-5}
$