F(n)=6n^2-3

Solution for F(n)=6n^2-3 equation:

(F)=6F^2-3

We move all terms to the left:

(F)-(6F^2-3)=0

We get rid of parentheses

-6F^2+F+3=0

a = -6; b = 1; c = +3;
Δ = b2-4ac
Δ = 12-4·(-6)·3
Δ = 73
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{73}}{2*-6}=\frac{-1-\sqrt{73}}{-12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{73}}{2*-6}=\frac{-1+\sqrt{73}}{-12}
$