F(x)=-3x^2-12x-5

Solution for F(x)=-3x^2-12x-5 equation:

(F)=-3F^2-12F-5

We move all terms to the left:

(F)-(-3F^2-12F-5)=0

We get rid of parentheses

3F^2+12F+F+5=0

We add all the numbers together, and all the variables

3F^2+13F+5=0

a = 3; b = 13; c = +5;
Δ = b2-4ac
Δ = 132-4·3·5
Δ = 109
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{109}}{2*3}=\frac{-13-\sqrt{109}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{109}}{2*3}=\frac{-13+\sqrt{109}}{6}
$