H(x)=5x^2-20+9

Solution for H(x)=5x^2-20+9 equation:

(H)=5H^2-20+9

We move all terms to the left:

(H)-(5H^2-20+9)=0

We get rid of parentheses

-5H^2+H+20-9=0

We add all the numbers together, and all the variables

-5H^2+H+11=0

a = -5; b = 1; c = +11;
Δ = b2-4ac
Δ = 12-4·(-5)·11
Δ = 221
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{221}}{2*-5}=\frac{-1-\sqrt{221}}{-10}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{221}}{2*-5}=\frac{-1+\sqrt{221}}{-10}
$