F(x)=-x^2-2x+7

Solution for F(x)=-x^2-2x+7 equation:

(F)=-F^2-2F+7

We move all terms to the left:

(F)-(-F^2-2F+7)=0

We get rid of parentheses

F^2+2F+F-7=0

We add all the numbers together, and all the variables

F^2+3F-7=0

a = 1; b = 3; c = -7;
Δ = b2-4ac
Δ = 32-4·1·(-7)
Δ = 37
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{-(3)-\sqrt{37}}{2*1}=\frac{-3-\sqrt{37}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{37}}{2*1}=\frac{-3+\sqrt{37}}{2}
$