F(x)=3x^2-27x+11

Solution for F(x)=3x^2-27x+11 equation:

(F)=3F^2-27F+11

We move all terms to the left:

(F)-(3F^2-27F+11)=0

We get rid of parentheses

-3F^2+F+27F-11=0

We add all the numbers together, and all the variables

-3F^2+28F-11=0

a = -3; b = 28; c = -11;
Δ = b2-4ac
Δ = 282-4·(-3)·(-11)
Δ = 652
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{652}=\sqrt{4*163}=\sqrt{4}*\sqrt{163}=2\sqrt{163}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{163}}{2*-3}=\frac{-28-2\sqrt{163}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{163}}{2*-3}=\frac{-28+2\sqrt{163}}{-6}
$