H=-16t^2+153t+90

Solution for H=-16t^2+153t+90 equation:

=-16H^2+153H+90

We move all terms to the left:

-(-16H^2+153H+90)=0

We get rid of parentheses

16H^2-153H-90=0

a = 16; b = -153; c = -90;
Δ = b2-4ac
Δ = -1532-4·16·(-90)
Δ = 29169
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:

$\sqrt{\Delta}=\sqrt{29169}=\sqrt{9*3241}=\sqrt{9}*\sqrt{3241}=3\sqrt{3241}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-153)-3\sqrt{3241}}{2*16}=\frac{153-3\sqrt{3241}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-153)+3\sqrt{3241}}{2*16}=\frac{153+3\sqrt{3241}}{32}
$