F(x)=2x-x2+3

Solution for F(x)=2x-x2+3 equation:

(F)=2F-F2+3

We move all terms to the left:

(F)-(2F-F2+3)=0

We add all the numbers together, and all the variables

-(+2F-1F^2+3)+F=0

We get rid of parentheses

1F^2-2F+F-3=0

We add all the numbers together, and all the variables

F^2-1F-3=0

a = 1; b = -1; c = -3;
Δ = b2-4ac
Δ = -12-4·1·(-3)
Δ = 13
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{13}}{2*1}=\frac{1-\sqrt{13}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{13}}{2*1}=\frac{1+\sqrt{13}}{2}
$