H=-5t^2-5t+90

Solution for H=-5t^2-5t+90 equation:

=-5H^2-5H+90

We move all terms to the left:

-(-5H^2-5H+90)=0

We get rid of parentheses

5H^2+5H-90=0

a = 5; b = 5; c = -90;
Δ = b2-4ac
Δ = 52-4·5·(-90)
Δ = 1825
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:

$\sqrt{\Delta}=\sqrt{1825}=\sqrt{25*73}=\sqrt{25}*\sqrt{73}=5\sqrt{73}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{73}}{2*5}=\frac{-5-5\sqrt{73}}{10}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{73}}{2*5}=\frac{-5+5\sqrt{73}}{10}
$