F(-5)=x^2-13x+37

Solution for F(-5)=x^2-13x+37 equation:

(-5)=F^2-13F+37

We move all terms to the left:

(-5)-(F^2-13F+37)=0

We add all the numbers together, and all the variables

-(F^2-13F+37)-5=0

We get rid of parentheses

-F^2+13F-37-5=0

We add all the numbers together, and all the variables

-1F^2+13F-42=0

a = -1; b = 13; c = -42;
Δ = b2-4ac
Δ = 132-4·(-1)·(-42)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-1}{2*-1}=\frac{-14}{-2}
=+7
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+1}{2*-1}=\frac{-12}{-2}
=+6
$