H(d)=-5d^2+70d+65

Solution for H(d)=-5d^2+70d+65 equation:

(H)=-5H^2+70H+65

We move all terms to the left:

(H)-(-5H^2+70H+65)=0

We get rid of parentheses

5H^2-70H+H-65=0

We add all the numbers together, and all the variables

5H^2-69H-65=0

a = 5; b = -69; c = -65;
Δ = b2-4ac
Δ = -692-4·5·(-65)
Δ = 6061
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{-(-69)-\sqrt{6061}}{2*5}=\frac{69-\sqrt{6061}}{10}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+\sqrt{6061}}{2*5}=\frac{69+\sqrt{6061}}{10}
$