F(x)=-2x2+2x+4

Solution for F(x)=-2x2+2x+4 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2F^2-1F-4=0

a = 2; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·2·(-4)
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{-(-1)-\sqrt{33}}{2*2}=\frac{1-\sqrt{33}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{33}}{2*2}=\frac{1+\sqrt{33}}{4}
$