H(x)=9x^2-5

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

(H)=9H^2-5

We move all terms to the left:

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

We get rid of parentheses

-9H^2+H+5=0

a = -9; b = 1; c = +5;
Δ = b2-4ac
Δ = 12-4·(-9)·5
Δ = 181
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{181}}{2*-9}=\frac{-1-\sqrt{181}}{-18}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{181}}{2*-9}=\frac{-1+\sqrt{181}}{-18}
$