F(x)=x2+12x+18

Solution for F(x)=x2+12x+18 equation:

(F)=F2+12F+18

We move all terms to the left:

(F)-(F2+12F+18)=0

We add all the numbers together, and all the variables

-(+F^2+12F+18)+F=0

We get rid of parentheses

-F^2-12F+F-18=0

We add all the numbers together, and all the variables

-1F^2-11F-18=0

a = -1; b = -11; c = -18;
Δ = b2-4ac
Δ = -112-4·(-1)·(-18)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-7}{2*-1}=\frac{4}{-2}
=-2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+7}{2*-1}=\frac{18}{-2}
=-9
$