H=-16t^2+256t+12

Solution for H=-16t^2+256t+12 equation:

=-16H^2+256H+12

We move all terms to the left:

-(-16H^2+256H+12)=0

We get rid of parentheses

16H^2-256H-12=0

a = 16; b = -256; c = -12;
Δ = b2-4ac
Δ = -2562-4·16·(-12)
Δ = 66304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{66304}=\sqrt{256*259}=\sqrt{256}*\sqrt{259}=16\sqrt{259}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-256)-16\sqrt{259}}{2*16}=\frac{256-16\sqrt{259}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-256)+16\sqrt{259}}{2*16}=\frac{256+16\sqrt{259}}{32}
$