F(x)=12x^2-54x+54

Solution for F(x)=12x^2-54x+54 equation:

(F)=12F^2-54F+54

We move all terms to the left:

(F)-(12F^2-54F+54)=0

We get rid of parentheses

-12F^2+F+54F-54=0

We add all the numbers together, and all the variables

-12F^2+55F-54=0

a = -12; b = 55; c = -54;
Δ = b2-4ac
Δ = 552-4·(-12)·(-54)
Δ = 433
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{-(55)-\sqrt{433}}{2*-12}=\frac{-55-\sqrt{433}}{-24}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{433}}{2*-12}=\frac{-55+\sqrt{433}}{-24}
$