0.1x^2-0.8x=0.9

Solution for 0.1x^2-0.8x=0.9 equation:

0.1x^2-0.8x=0.9

We move all terms to the left:

0.1x^2-0.8x-(0.9)=0

We add all the numbers together, and all the variables

0.1x^2-0.8x-0.9=0

a = 0.1; b = -0.8; c = -0.9;
Δ = b2-4ac
Δ = -0.82-4·0.1·(-0.9)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.8)-1}{2*0.1}=\frac{-0.2}{0.2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.8)+1}{2*0.1}=\frac{1.8}{0.2}
=9
$