Y=-16x^2+112x+8

Solution for Y=-16x^2+112x+8 equation:

=-16Y^2+112Y+8

We move all terms to the left:

-(-16Y^2+112Y+8)=0

We get rid of parentheses

16Y^2-112Y-8=0

a = 16; b = -112; c = -8;
Δ = b2-4ac
Δ = -1122-4·16·(-8)
Δ = 13056
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:

$\sqrt{\Delta}=\sqrt{13056}=\sqrt{256*51}=\sqrt{256}*\sqrt{51}=16\sqrt{51}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-16\sqrt{51}}{2*16}=\frac{112-16\sqrt{51}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+16\sqrt{51}}{2*16}=\frac{112+16\sqrt{51}}{32}
$