F(-5)=x^2-2x-7

Solution for F(-5)=x^2-2x-7 equation:

(-5)=F^2-2F-7

We move all terms to the left:

(-5)-(F^2-2F-7)=0

We add all the numbers together, and all the variables

-(F^2-2F-7)-5=0

We get rid of parentheses

-F^2+2F+7-5=0

We add all the numbers together, and all the variables

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

a = -1; b = 2; c = +2;
Δ = b2-4ac
Δ = 22-4·(-1)·2
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{3}}{2*-1}=\frac{-2-2\sqrt{3}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{3}}{2*-1}=\frac{-2+2\sqrt{3}}{-2}
$