H=16t^2+50t+6

Solution for H=16t^2+50t+6 equation:

=16H^2+50H+6

We move all terms to the left:

-(16H^2+50H+6)=0

We get rid of parentheses

-16H^2-50H-6=0

a = -16; b = -50; c = -6;
Δ = b2-4ac
Δ = -502-4·(-16)·(-6)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-46}{2*-16}=\frac{4}{-32}
=-1/8
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+46}{2*-16}=\frac{96}{-32}
=-3
$