F(x)=12x^2-1

Solution for F(x)=12x^2-1 equation:

(F)=12F^2-1

We move all terms to the left:

(F)-(12F^2-1)=0

We get rid of parentheses

-12F^2+F+1=0

a = -12; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-12)·1
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*-12}=\frac{-8}{-24}
=1/3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*-12}=\frac{6}{-24}
=-1/4
$