0.1x^2-0.8x-0.1=-0.2

Solution for 0.1x^2-0.8x-0.1=-0.2 equation:

0.1x^2-0.8x-0.1=-0.2

We move all terms to the left:

0.1x^2-0.8x-0.1-(-0.2)=0

We add all the numbers together, and all the variables

0.1x^2-0.8x+0.1=0

a = 0.1; b = -0.8; c = +0.1;
Δ = b2-4ac
Δ = -0.82-4·0.1·0.1
Δ = 0.6
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.8)-\sqrt{0.6}}{2*0.1}=\frac{0.8-\sqrt{0.6}}{0.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.8)+\sqrt{0.6}}{2*0.1}=\frac{0.8+\sqrt{0.6}}{0.2}
$