F(x)=-x2+6x+27

Solution for F(x)=-x2+6x+27 equation:

(F)=-F2+6F+27

We move all terms to the left:

(F)-(-F2+6F+27)=0

We add all the numbers together, and all the variables

-(-1F^2+6F+27)+F=0

We get rid of parentheses

1F^2-6F+F-27=0

We add all the numbers together, and all the variables

F^2-5F-27=0

a = 1; b = -5; c = -27;
Δ = b2-4ac
Δ = -52-4·1·(-27)
Δ = 133
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{-(-5)-\sqrt{133}}{2*1}=\frac{5-\sqrt{133}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{133}}{2*1}=\frac{5+\sqrt{133}}{2}
$