Y=-16x^2-40x+5

Solution for Y=-16x^2-40x+5 equation:

=-16Y^2-40Y+5

We move all terms to the left:

-(-16Y^2-40Y+5)=0

We get rid of parentheses

16Y^2+40Y-5=0

a = 16; b = 40; c = -5;
Δ = b2-4ac
Δ = 402-4·16·(-5)
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{30}}{2*16}=\frac{-40-8\sqrt{30}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{30}}{2*16}=\frac{-40+8\sqrt{30}}{32}
$