F(x)=-2x^2+-8x+4

Solution for F(x)=-2x^2+-8x+4 equation:

(F)=-2F^2+-8F+4

We move all terms to the left:

(F)-(-2F^2+-8F+4)=0

We use the square of the difference formula

-(-2F^2-8F+4)+F=0

We get rid of parentheses

2F^2+8F+F-4=0

We add all the numbers together, and all the variables

2F^2+9F-4=0

a = 2; b = 9; c = -4;
Δ = b2-4ac
Δ = 92-4·2·(-4)
Δ = 113
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{-(9)-\sqrt{113}}{2*2}=\frac{-9-\sqrt{113}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{113}}{2*2}=\frac{-9+\sqrt{113}}{4}
$