H=-16t^2+12t+88

Solution for H=-16t^2+12t+88 equation:

=-16H^2+12H+88

We move all terms to the left:

-(-16H^2+12H+88)=0

We get rid of parentheses

16H^2-12H-88=0

a = 16; b = -12; c = -88;
Δ = b2-4ac
Δ = -122-4·16·(-88)
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-76}{2*16}=\frac{-64}{32}
=-2
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+76}{2*16}=\frac{88}{32}
=2+3/4
$