H=-16t^2+12t+75

Solution for H=-16t^2+12t+75 equation:

=-16H^2+12H+75

We move all terms to the left:

-(-16H^2+12H+75)=0

We get rid of parentheses

16H^2-12H-75=0

a = 16; b = -12; c = -75;
Δ = b2-4ac
Δ = -122-4·16·(-75)
Δ = 4944
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:

$\sqrt{\Delta}=\sqrt{4944}=\sqrt{16*309}=\sqrt{16}*\sqrt{309}=4\sqrt{309}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{309}}{2*16}=\frac{12-4\sqrt{309}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{309}}{2*16}=\frac{12+4\sqrt{309}}{32}
$