H=-4.9t^2+58.8t

Solution for H=-4.9t^2+58.8t equation:

=-4.9H^2+58.8H

We move all terms to the left:

-(-4.9H^2+58.8H)=0

We get rid of parentheses

4.9H^2-58.8H=0

a = 4.9; b = -58.8; c = 0;
Δ = b2-4ac
Δ = -58.82-4·4.9·0
Δ = 3457.44
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{-(-58.8)-\sqrt{3457.44}}{2*4.9}=\frac{58.8-\sqrt{3457.44}}{9.8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58.8)+\sqrt{3457.44}}{2*4.9}=\frac{58.8+\sqrt{3457.44}}{9.8}
$