F(8)=9x^2-1

Solution for F(8)=9x^2-1 equation:

(8)=9F^2-1

We move all terms to the left:

(8)-(9F^2-1)=0

We get rid of parentheses

-9F^2+1+8=0

We add all the numbers together, and all the variables

-9F^2+9=0

a = -9; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-9)·9
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18}{2*-9}=\frac{-18}{-18}
=1
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18}{2*-9}=\frac{18}{-18}
=-1
$