F(-6)=-x^2-4x+5

Solution for F(-6)=-x^2-4x+5 equation:

(-6)=-F^2-4F+5

We move all terms to the left:

(-6)-(-F^2-4F+5)=0

We add all the numbers together, and all the variables

-(-F^2-4F+5)-6=0

We get rid of parentheses

F^2+4F-5-6=0

We add all the numbers together, and all the variables

F^2+4F-11=0

a = 1; b = 4; c = -11;
Δ = b2-4ac
Δ = 42-4·1·(-11)
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{15}}{2*1}=\frac{-4-2\sqrt{15}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{15}}{2*1}=\frac{-4+2\sqrt{15}}{2}
$