F(-2)=5x-2x^2

Solution for F(-2)=5x-2x^2 equation:

(-2)=5F-2F^2

We move all terms to the left:

(-2)-(5F-2F^2)=0

We add all the numbers together, and all the variables

-(5F-2F^2)-2=0

We get rid of parentheses

2F^2-5F-2=0

a = 2; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·2·(-2)
Δ = 41
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{41}}{2*2}=\frac{5-\sqrt{41}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{41}}{2*2}=\frac{5+\sqrt{41}}{4}
$