H(t)=-16t^2+90t+46

Solution for H(t)=-16t^2+90t+46 equation:

(H)=-16H^2+90H+46

We move all terms to the left:

(H)-(-16H^2+90H+46)=0

We get rid of parentheses

16H^2-90H+H-46=0

We add all the numbers together, and all the variables

16H^2-89H-46=0

a = 16; b = -89; c = -46;
Δ = b2-4ac
Δ = -892-4·16·(-46)
Δ = 10865
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-89)-\sqrt{10865}}{2*16}=\frac{89-\sqrt{10865}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+\sqrt{10865}}{2*16}=\frac{89+\sqrt{10865}}{32}
$