Y=-20x^2-400x-24

Solution for Y=-20x^2-400x-24 equation:

=-20Y^2-400Y-24

We move all terms to the left:

-(-20Y^2-400Y-24)=0

We get rid of parentheses

20Y^2+400Y+24=0

a = 20; b = 400; c = +24;
Δ = b2-4ac
Δ = 4002-4·20·24
Δ = 158080
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:

$\sqrt{\Delta}=\sqrt{158080}=\sqrt{64*2470}=\sqrt{64}*\sqrt{2470}=8\sqrt{2470}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-8\sqrt{2470}}{2*20}=\frac{-400-8\sqrt{2470}}{40}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+8\sqrt{2470}}{2*20}=\frac{-400+8\sqrt{2470}}{40}
$