3.8(x-x^2)=0.9

Solution for 3.8(x-x^2)=0.9 equation:

3.8(x-x^2)=0.9

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-3.8x^2+3.8x-0.9=0

a = -3.8; b = 3.8; c = -0.9;
Δ = b2-4ac
Δ = 3.82-4·(-3.8)·(-0.9)
Δ = 0.76
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{-(3.8)-\sqrt{0.76}}{2*-3.8}=\frac{-3.8-\sqrt{0.76}}{-7.6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3.8)+\sqrt{0.76}}{2*-3.8}=\frac{-3.8+\sqrt{0.76}}{-7.6}
$