0=-4x+0.1x^2

Solution for 0=-4x+0.1x^2 equation:

0=-4x+0.1x^2

We move all terms to the left:

0-(-4x+0.1x^2)=0

We add all the numbers together, and all the variables

-(-4x+0.1x^2)=0

We get rid of parentheses

-0.1x^2+4x=0

a = -0.1; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-0.1)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-0.1}=\frac{-8}{-0.2}
=+40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-0.1}=\frac{0}{-0.2}
=0
$