400y-y^2=10000

Solution for 400y-y^2=10000 equation:

400y-y^2=10000

We move all terms to the left:

400y-y^2-(10000)=0

We add all the numbers together, and all the variables

-1y^2+400y-10000=0

a = -1; b = 400; c = -10000;
Δ = b2-4ac
Δ = 4002-4·(-1)·(-10000)
Δ = 120000
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:

$\sqrt{\Delta}=\sqrt{120000}=\sqrt{40000*3}=\sqrt{40000}*\sqrt{3}=200\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-200\sqrt{3}}{2*-1}=\frac{-400-200\sqrt{3}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+200\sqrt{3}}{2*-1}=\frac{-400+200\sqrt{3}}{-2}
$