H=-5t2+192

Solution for H=-5t2+192 equation:

=-5H^2+192

We move all terms to the left:

-(-5H^2+192)=0

We get rid of parentheses

5H^2-192=0

a = 5; b = 0; c = -192;
Δ = b2-4ac
Δ = 02-4·5·(-192)
Δ = 3840
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{15}}{2*5}=\frac{0-16\sqrt{15}}{10}
=-\frac{16\sqrt{15}}{10}
=-\frac{8\sqrt{15}}{5}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{15}}{2*5}=\frac{0+16\sqrt{15}}{10}
=\frac{16\sqrt{15}}{10}
=\frac{8\sqrt{15}}{5}
$