F(x)=x^2-14x+54

Solution for F(x)=x^2-14x+54 equation:

(F)=F^2-14F+54

We move all terms to the left:

(F)-(F^2-14F+54)=0

We get rid of parentheses

-F^2+F+14F-54=0

We add all the numbers together, and all the variables

-1F^2+15F-54=0

a = -1; b = 15; c = -54;
Δ = b2-4ac
Δ = 152-4·(-1)·(-54)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3}{2*-1}=\frac{-18}{-2}
=+9
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3}{2*-1}=\frac{-12}{-2}
=+6
$