F(x)=3x^2+9x-54

Solution for F(x)=3x^2+9x-54 equation:

(F)=3F^2+9F-54

We move all terms to the left:

(F)-(3F^2+9F-54)=0

We get rid of parentheses

-3F^2+F-9F+54=0

We add all the numbers together, and all the variables

-3F^2-8F+54=0

a = -3; b = -8; c = +54;
Δ = b2-4ac
Δ = -82-4·(-3)·54
Δ = 712
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:

$\sqrt{\Delta}=\sqrt{712}=\sqrt{4*178}=\sqrt{4}*\sqrt{178}=2\sqrt{178}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{178}}{2*-3}=\frac{8-2\sqrt{178}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{178}}{2*-3}=\frac{8+2\sqrt{178}}{-6}
$