H=-5t^2+30t+200

Solution for H=-5t^2+30t+200 equation:

=-5H^2+30H+200

We move all terms to the left:

-(-5H^2+30H+200)=0

We get rid of parentheses

5H^2-30H-200=0

a = 5; b = -30; c = -200;
Δ = b2-4ac
Δ = -302-4·5·(-200)
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-70}{2*5}=\frac{-40}{10}
=-4
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+70}{2*5}=\frac{100}{10}
=10
$