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

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

(F)=-F2+8F-4

We move all terms to the left:

(F)-(-F2+8F-4)=0

We add all the numbers together, and all the variables

-(-1F^2+8F-4)+F=0

We get rid of parentheses

1F^2-8F+F+4=0

We add all the numbers together, and all the variables

F^2-7F+4=0

a = 1; b = -7; c = +4;
Δ = b2-4ac
Δ = -72-4·1·4
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{-(-7)-\sqrt{33}}{2*1}=\frac{7-\sqrt{33}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{33}}{2*1}=\frac{7+\sqrt{33}}{2}
$