H=4.8t^2+43.2t

Solution for H=4.8t^2+43.2t equation:

=4.8H^2+43.2H

We move all terms to the left:

-(4.8H^2+43.2H)=0

We get rid of parentheses

-4.8H^2-43.2H=0

a = -4.8; b = -43.2; c = 0;
Δ = b2-4ac
Δ = -43.22-4·(-4.8)·0
Δ = 1866.24
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{-(-43.2)-\sqrt{1866.24}}{2*-4.8}=\frac{43.2-\sqrt{1866.24}}{-9.6}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43.2)+\sqrt{1866.24}}{2*-4.8}=\frac{43.2+\sqrt{1866.24}}{-9.6}
$