F(x)=10000-250x2

Solution for F(x)=10000-250x2 equation:

(F)=10000-250F^2

We move all terms to the left:

(F)-(10000-250F^2)=0

We get rid of parentheses

250F^2+F-10000=0

a = 250; b = 1; c = -10000;
Δ = b2-4ac
Δ = 12-4·250·(-10000)
Δ = 10000001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{10000001}}{2*250}=\frac{-1-\sqrt{10000001}}{500}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{10000001}}{2*250}=\frac{-1+\sqrt{10000001}}{500}
$