H(x)=4x2-9

Solution for H(x)=4x2-9 equation:

(H)=4H^2-9

We move all terms to the left:

(H)-(4H^2-9)=0

We get rid of parentheses

-4H^2+H+9=0

a = -4; b = 1; c = +9;
Δ = b2-4ac
Δ = 12-4·(-4)·9
Δ = 145
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{145}}{2*-4}=\frac{-1-\sqrt{145}}{-8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{145}}{2*-4}=\frac{-1+\sqrt{145}}{-8}
$