F(x)=-2x^2-4x+1

Solution for F(x)=-2x^2-4x+1 equation:

(F)=-2F^2-4F+1

We move all terms to the left:

(F)-(-2F^2-4F+1)=0

We get rid of parentheses

2F^2+4F+F-1=0

We add all the numbers together, and all the variables

2F^2+5F-1=0

a = 2; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·2·(-1)
Δ = 33
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{-(5)-\sqrt{33}}{2*2}=\frac{-5-\sqrt{33}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{33}}{2*2}=\frac{-5+\sqrt{33}}{4}
$