F(2)=x^2+6x-27

Solution for F(2)=x^2+6x-27 equation:

(2)=F^2+6F-27

We move all terms to the left:

(2)-(F^2+6F-27)=0

We get rid of parentheses

-F^2-6F+27+2=0

We add all the numbers together, and all the variables

-1F^2-6F+29=0

a = -1; b = -6; c = +29;
Δ = b2-4ac
Δ = -62-4·(-1)·29
Δ = 152
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:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{38}}{2*-1}=\frac{6-2\sqrt{38}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{38}}{2*-1}=\frac{6+2\sqrt{38}}{-2}
$