F(x)=-4x^2-12x

Solution for F(x)=-4x^2-12x equation:

(F)=-4F^2-12F

We move all terms to the left:

(F)-(-4F^2-12F)=0

We get rid of parentheses

4F^2+12F+F=0

We add all the numbers together, and all the variables

4F^2+13F=0

a = 4; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·4·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*4}=\frac{-26}{8}
=-3+1/4
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*4}=\frac{0}{8}
=0
$