H=37+7t-4.9t^2

Solution for H=37+7t-4.9t^2 equation:

=37+7H-4.9H^2

We move all terms to the left:

-(37+7H-4.9H^2)=0

We get rid of parentheses

4.9H^2-7H-37=0

a = 4.9; b = -7; c = -37;
Δ = b2-4ac
Δ = -72-4·4.9·(-37)
Δ = 774.2
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{-(-7)-\sqrt{774.2}}{2*4.9}=\frac{7-\sqrt{774.2}}{9.8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{774.2}}{2*4.9}=\frac{7+\sqrt{774.2}}{9.8}
$