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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2F^2-4F-1=0

a = 2; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·2·(-1)
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{6}}{2*2}=\frac{4-2\sqrt{6}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{6}}{2*2}=\frac{4+2\sqrt{6}}{4}
$