H=-16t2+46t-9

Solution for H=-16t2+46t-9 equation:

=-16H^2+46H-9

We move all terms to the left:

-(-16H^2+46H-9)=0

We get rid of parentheses

16H^2-46H+9=0

a = 16; b = -46; c = +9;
Δ = b2-4ac
Δ = -462-4·16·9
Δ = 1540
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1540}=\sqrt{4*385}=\sqrt{4}*\sqrt{385}=2\sqrt{385}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{385}}{2*16}=\frac{46-2\sqrt{385}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{385}}{2*16}=\frac{46+2\sqrt{385}}{32}
$