F(x)=x2-12x+14

Solution for F(x)=x2-12x+14 equation:

(F)=F2-12F+14

We move all terms to the left:

(F)-(F2-12F+14)=0

We add all the numbers together, and all the variables

-(+F^2-12F+14)+F=0

We get rid of parentheses

-F^2+12F+F-14=0

We add all the numbers together, and all the variables

-1F^2+13F-14=0

a = -1; b = 13; c = -14;
Δ = b2-4ac
Δ = 132-4·(-1)·(-14)
Δ = 113
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{113}}{2*-1}=\frac{-13-\sqrt{113}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{113}}{2*-1}=\frac{-13+\sqrt{113}}{-2}
$