F(x)=-2x2+4x+8

Solution for F(x)=-2x2+4x+8 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2F^2-3F-8=0

a = 2; b = -3; c = -8;
Δ = b2-4ac
Δ = -32-4·2·(-8)
Δ = 73
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{-(-3)-\sqrt{73}}{2*2}=\frac{3-\sqrt{73}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{73}}{2*2}=\frac{3+\sqrt{73}}{4}
$