F(n)=-0,25n2-0,5n+1

Solution for F(n)=-0,25n2-0,5n+1 equation:

(F)=-0.25F^2-0.5F+1

We move all terms to the left:

(F)-(-0.25F^2-0.5F+1)=0

We get rid of parentheses

0.25F^2+0.5F+F-1=0

We add all the numbers together, and all the variables

0.25F^2+1.5F-1=0

a = 0.25; b = 1.5; c = -1;
Δ = b2-4ac
Δ = 1.52-4·0.25·(-1)
Δ = 3.25
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{-(1.5)-\sqrt{3.25}}{2*0.25}=\frac{-1.5-\sqrt{3.25}}{0.5}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{3.25}}{2*0.25}=\frac{-1.5+\sqrt{3.25}}{0.5}
$