F(x)=8x^2-1

Solution for F(x)=8x^2-1 equation:

(F)=8F^2-1

We move all terms to the left:

(F)-(8F^2-1)=0

We get rid of parentheses

-8F^2+F+1=0

a = -8; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-8)·1
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{33}}{2*-8}=\frac{-1-\sqrt{33}}{-16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{33}}{2*-8}=\frac{-1+\sqrt{33}}{-16}
$