Y=-16x^2+4x+382

Solution for Y=-16x^2+4x+382 equation:

=-16Y^2+4Y+382

We move all terms to the left:

-(-16Y^2+4Y+382)=0

We get rid of parentheses

16Y^2-4Y-382=0

a = 16; b = -4; c = -382;
Δ = b2-4ac
Δ = -42-4·16·(-382)
Δ = 24464
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:

$\sqrt{\Delta}=\sqrt{24464}=\sqrt{16*1529}=\sqrt{16}*\sqrt{1529}=4\sqrt{1529}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{1529}}{2*16}=\frac{4-4\sqrt{1529}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{1529}}{2*16}=\frac{4+4\sqrt{1529}}{32}
$