H(t)=155-15t-5t^2

Solution for H(t)=155-15t-5t^2 equation:

(H)=155-15H-5H^2

We move all terms to the left:

(H)-(155-15H-5H^2)=0

We get rid of parentheses

5H^2+15H+H-155=0

We add all the numbers together, and all the variables

5H^2+16H-155=0

a = 5; b = 16; c = -155;
Δ = b2-4ac
Δ = 162-4·5·(-155)
Δ = 3356
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:

$\sqrt{\Delta}=\sqrt{3356}=\sqrt{4*839}=\sqrt{4}*\sqrt{839}=2\sqrt{839}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{839}}{2*5}=\frac{-16-2\sqrt{839}}{10}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{839}}{2*5}=\frac{-16+2\sqrt{839}}{10}
$