H(t)=-6t^2-12t+90

Solution for H(t)=-6t^2-12t+90 equation:

(H)=-6H^2-12H+90

We move all terms to the left:

(H)-(-6H^2-12H+90)=0

We get rid of parentheses

6H^2+12H+H-90=0

We add all the numbers together, and all the variables

6H^2+13H-90=0

a = 6; b = 13; c = -90;
Δ = b2-4ac
Δ = 132-4·6·(-90)
Δ = 2329
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{-(13)-\sqrt{2329}}{2*6}=\frac{-13-\sqrt{2329}}{12}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{2329}}{2*6}=\frac{-13+\sqrt{2329}}{12}
$