H(t)=100t+-16t2

Solution for H(t)=100t+-16t2 equation:

(H)=100H+-16H^2

We move all terms to the left:

(H)-(100H+-16H^2)=0

We use the square of the difference formula

-(100H-16H^2)+H=0

We get rid of parentheses

16H^2-100H+H=0

We add all the numbers together, and all the variables

16H^2-99H=0

a = 16; b = -99; c = 0;
Δ = b2-4ac
Δ = -992-4·16·0
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-99}{2*16}=\frac{0}{32}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+99}{2*16}=\frac{198}{32}
=6+3/16
$