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

Solution for F(0)=2x^2+x-1 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-2F^2-F+1=0

We add all the numbers together, and all the variables

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

a = -2; b = -1; c = +1;
Δ = b2-4ac
Δ = -12-4·(-2)·1
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3}{2*-2}=\frac{-2}{-4}
=1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3}{2*-2}=\frac{4}{-4}
=-1
$