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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2F^2-11F-6=0

a = -2; b = -11; c = -6;
Δ = b2-4ac
Δ = -112-4·(-2)·(-6)
Δ = 73
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{-(-11)-\sqrt{73}}{2*-2}=\frac{11-\sqrt{73}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{73}}{2*-2}=\frac{11+\sqrt{73}}{-4}
$