F(x)=0.5-2x2

Solution for F(x)=0.5-2x2 equation:

(F)=0.5-2F^2

We move all terms to the left:

(F)-(0.5-2F^2)=0

We get rid of parentheses

2F^2+F-0.5=0

a = 2; b = 1; c = -0.5;
Δ = b2-4ac
Δ = 12-4·2·(-0.5)
Δ = 5
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{5}}{2*2}=\frac{-1-\sqrt{5}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{5}}{2*2}=\frac{-1+\sqrt{5}}{4}
$