F(x)=-x2+2x+6

Solution for F(x)=-x2+2x+6 equation:

(F)=-F2+2F+6

We move all terms to the left:

(F)-(-F2+2F+6)=0

We add all the numbers together, and all the variables

-(-1F^2+2F+6)+F=0

We get rid of parentheses

1F^2-2F+F-6=0

We add all the numbers together, and all the variables

F^2-1F-6=0

a = 1; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·1·(-6)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*1}=\frac{-4}{2}
=-2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*1}=\frac{6}{2}
=3
$