F(x)=-x^2-6x+12

Solution for F(x)=-x^2-6x+12 equation:

(F)=-F^2-6F+12

We move all terms to the left:

(F)-(-F^2-6F+12)=0

We get rid of parentheses

F^2+6F+F-12=0

We add all the numbers together, and all the variables

F^2+7F-12=0

a = 1; b = 7; c = -12;
Δ = b2-4ac
Δ = 72-4·1·(-12)
Δ = 97
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{-(7)-\sqrt{97}}{2*1}=\frac{-7-\sqrt{97}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{97}}{2*1}=\frac{-7+\sqrt{97}}{2}
$