Y=10000-250x^2

Solution for Y=10000-250x^2 equation:

=10000-250Y^2

We move all terms to the left:

-(10000-250Y^2)=0

We get rid of parentheses

250Y^2-10000=0

a = 250; b = 0; c = -10000;
Δ = b2-4ac
Δ = 02-4·250·(-10000)
Δ = 10000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10000000}=\sqrt{1000000*10}=\sqrt{1000000}*\sqrt{10}=1000\sqrt{10}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1000\sqrt{10}}{2*250}=\frac{0-1000\sqrt{10}}{500}
=-\frac{1000\sqrt{10}}{500}
=-2\sqrt{10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1000\sqrt{10}}{2*250}=\frac{0+1000\sqrt{10}}{500}
=\frac{1000\sqrt{10}}{500}
=2\sqrt{10}
$