H=-16t2+46t+6

Solution for H=-16t2+46t+6 equation:

=-16H^2+46H+6

We move all terms to the left:

-(-16H^2+46H+6)=0

We get rid of parentheses

16H^2-46H-6=0

a = 16; b = -46; c = -6;
Δ = b2-4ac
Δ = -462-4·16·(-6)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-50}{2*16}=\frac{-4}{32}
=-1/8
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+50}{2*16}=\frac{96}{32}
=3
$