H(x)=25x^2-1

Solution for H(x)=25x^2-1 equation:

(H)=25H^2-1

We move all terms to the left:

(H)-(25H^2-1)=0

We get rid of parentheses

-25H^2+H+1=0

a = -25; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-25)·1
Δ = 101
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{101}}{2*-25}=\frac{-1-\sqrt{101}}{-50}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{101}}{2*-25}=\frac{-1+\sqrt{101}}{-50}
$