0.8*x-x^2=0.12

Solution for 0.8*x-x^2=0.12 equation:

0.8x-x^2=0.12

We move all terms to the left:

0.8x-x^2-(0.12)=0

We add all the numbers together, and all the variables

-1x^2+0.8x-0.12=0

a = -1; b = 0.8; c = -0.12;
Δ = b2-4ac
Δ = 0.82-4·(-1)·(-0.12)
Δ = 0.16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.8)-\sqrt{0.16}}{2*-1}=\frac{-0.8-\sqrt{0.16}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.8)+\sqrt{0.16}}{2*-1}=\frac{-0.8+\sqrt{0.16}}{-2}
$