x-(0.1x^2)=0.6

Solution for x-(0.1x^2)=0.6 equation:

x-(0.1x^2)=0.6

We move all terms to the left:

x-(0.1x^2)-(0.6)=0

We add all the numbers together, and all the variables

x-(0.1x^2)-0.6=0

We get rid of parentheses

-0.1x^2+x-0.6=0

a = -0.1; b = 1; c = -0.6;
Δ = b2-4ac
Δ = 12-4·(-0.1)·(-0.6)
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{-(1)-\sqrt{0.76}}{2*-0.1}=\frac{-1-\sqrt{0.76}}{-0.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{0.76}}{2*-0.1}=\frac{-1+\sqrt{0.76}}{-0.2}
$