F(x)=-2x^2+8x-1

Solution for F(x)=-2x^2+8x-1 equation:

(F)=-2F^2+8F-1

We move all terms to the left:

(F)-(-2F^2+8F-1)=0

We get rid of parentheses

2F^2-8F+F+1=0

We add all the numbers together, and all the variables

2F^2-7F+1=0

a = 2; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·2·1
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{-(-7)-\sqrt{41}}{2*2}=\frac{7-\sqrt{41}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{41}}{2*2}=\frac{7+\sqrt{41}}{4}
$