H=197-21t-16t^2

Solution for H=197-21t-16t^2 equation:

=197-21H-16H^2

We move all terms to the left:

-(197-21H-16H^2)=0

We get rid of parentheses

16H^2+21H-197=0

a = 16; b = 21; c = -197;
Δ = b2-4ac
Δ = 212-4·16·(-197)
Δ = 13049
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{-(21)-\sqrt{13049}}{2*16}=\frac{-21-\sqrt{13049}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{13049}}{2*16}=\frac{-21+\sqrt{13049}}{32}
$