F(x)=1.5-12*x-6*x^2

Solution for F(x)=1.5-12*x-6*x^2 equation:

(F)=1.5-12F-6F^2

We move all terms to the left:

(F)-(1.5-12F-6F^2)=0

We get rid of parentheses

6F^2+12F+F-1.5=0

We add all the numbers together, and all the variables

6F^2+13F-1.5=0

a = 6; b = 13; c = -1.5;
Δ = b2-4ac
Δ = 132-4·6·(-1.5)
Δ = 205
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{-(13)-\sqrt{205}}{2*6}=\frac{-13-\sqrt{205}}{12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{205}}{2*6}=\frac{-13+\sqrt{205}}{12}
$