H(t)=-16t^2+48t+50t

Solution for H(t)=-16t^2+48t+50t equation:

(H)=-16H^2+48H+50H

We move all terms to the left:

(H)-(-16H^2+48H+50H)=0

We get rid of parentheses

16H^2-48H-50H+H=0

We add all the numbers together, and all the variables

16H^2-97H=0

a = 16; b = -97; c = 0;
Δ = b2-4ac
Δ = -972-4·16·0
Δ = 9409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9409}=97$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-97)-97}{2*16}=\frac{0}{32}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-97)+97}{2*16}=\frac{194}{32}
=6+1/16
$