F(x)=-x^2+2x+10

Solution for F(x)=-x^2+2x+10 equation:

(F)=-F^2+2F+10

We move all terms to the left:

(F)-(-F^2+2F+10)=0

We get rid of parentheses

F^2-2F+F-10=0

We add all the numbers together, and all the variables

F^2-1F-10=0

a = 1; b = -1; c = -10;
Δ = b2-4ac
Δ = -12-4·1·(-10)
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{-(-1)-\sqrt{41}}{2*1}=\frac{1-\sqrt{41}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{41}}{2*1}=\frac{1+\sqrt{41}}{2}
$