H(x)=45-0.01x2

Solution for H(x)=45-0.01x2 equation:

(H)=45-0.01H^2

We move all terms to the left:

(H)-(45-0.01H^2)=0

We get rid of parentheses

0.01H^2+H-45=0

a = 0.01; b = 1; c = -45;
Δ = b2-4ac
Δ = 12-4·0.01·(-45)
Δ = 2.8
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{-(1)-\sqrt{2.8}}{2*0.01}=\frac{-1-\sqrt{2.8}}{0.02}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{2.8}}{2*0.01}=\frac{-1+\sqrt{2.8}}{0.02}
$