2x-x^2=0.9

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

2x-x^2=0.9

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1x^2+2x-0.9=0

a = -1; b = 2; c = -0.9;
Δ = b2-4ac
Δ = 22-4·(-1)·(-0.9)
Δ = 0.4
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{-(2)-\sqrt{0.4}}{2*-1}=\frac{-2-\sqrt{0.4}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+\sqrt{0.4}}{2*-1}=\frac{-2+\sqrt{0.4}}{-2}
$