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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1F^2+6F+7=0

a = -1; b = 6; c = +7;
Δ = b2-4ac
Δ = 62-4·(-1)·7
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-8}{2*-1}=\frac{-14}{-2}
=+7
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+8}{2*-1}=\frac{2}{-2}
=-1
$