H=40-5x-5x^2

Solution for H=40-5x-5x^2 equation:

=40-5H-5H^2

We move all terms to the left:

-(40-5H-5H^2)=0

We get rid of parentheses

5H^2+5H-40=0

a = 5; b = 5; c = -40;
Δ = b2-4ac
Δ = 52-4·5·(-40)
Δ = 825
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:

$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{33}}{2*5}=\frac{-5-5\sqrt{33}}{10}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{33}}{2*5}=\frac{-5+5\sqrt{33}}{10}
$