F(n)=3n2-7

Solution for F(n)=3n2-7 equation:

(F)=3F^2-7

We move all terms to the left:

(F)-(3F^2-7)=0

We get rid of parentheses

-3F^2+F+7=0

a = -3; b = 1; c = +7;
Δ = b2-4ac
Δ = 12-4·(-3)·7
Δ = 85
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{85}}{2*-3}=\frac{-1-\sqrt{85}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{85}}{2*-3}=\frac{-1+\sqrt{85}}{-6}
$