F(n)=25-2n^2

Solution for F(n)=25-2n^2 equation:

(F)=25-2F^2

We move all terms to the left:

(F)-(25-2F^2)=0

We get rid of parentheses

2F^2+F-25=0

a = 2; b = 1; c = -25;
Δ = b2-4ac
Δ = 12-4·2·(-25)
Δ = 201
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{201}}{2*2}=\frac{-1-\sqrt{201}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{201}}{2*2}=\frac{-1+\sqrt{201}}{4}
$