x-0.0002(x^2)=250

Solution for x-0.0002(x^2)=250 equation:

x-0.0002(x^2)=250

We move all terms to the left:

x-0.0002(x^2)-(250)=0

determiningTheFunctionDomain
-0.0002x^2+x-250=0

a = -0.0002; b = 1; c = -250;
Δ = b2-4ac
Δ = 12-4·(-0.0002)·(-250)
Δ = 0.8
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{0.8}}{2*-0.0002}=\frac{-1-\sqrt{0.8}}{-0.0004}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{0.8}}{2*-0.0002}=\frac{-1+\sqrt{0.8}}{-0.0004}
$