F(x)=x^2-12x+5

Solution for F(x)=x^2-12x+5 equation:

(F)=F^2-12F+5

We move all terms to the left:

(F)-(F^2-12F+5)=0

We get rid of parentheses

-F^2+F+12F-5=0

We add all the numbers together, and all the variables

-1F^2+13F-5=0

a = -1; b = 13; c = -5;
Δ = b2-4ac
Δ = 132-4·(-1)·(-5)
Δ = 149
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{-(13)-\sqrt{149}}{2*-1}=\frac{-13-\sqrt{149}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{149}}{2*-1}=\frac{-13+\sqrt{149}}{-2}
$