H=16t^2-21t-197

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

=16H^2-21H-197

We move all terms to the left:

-(16H^2-21H-197)=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}
$