H=-4.9t^2+47t

Solution for H=-4.9t^2+47t equation:

=-4.9H^2+47H

We move all terms to the left:

-(-4.9H^2+47H)=0

We get rid of parentheses

4.9H^2-47H=0

a = 4.9; b = -47; c = 0;
Δ = b2-4ac
Δ = -472-4·4.9·0
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-47}{2*4.9}=\frac{0}{9.8}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+47}{2*4.9}=\frac{94}{9.8}
=9+3.2222222222222/5.4444444444445
$