F(x)=-3x^2-15x-12

Solution for F(x)=-3x^2-15x-12 equation:

(F)=-3F^2-15F-12

We move all terms to the left:

(F)-(-3F^2-15F-12)=0

We get rid of parentheses

3F^2+15F+F+12=0

We add all the numbers together, and all the variables

3F^2+16F+12=0

a = 3; b = 16; c = +12;
Δ = b2-4ac
Δ = 162-4·3·12
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{7}}{2*3}=\frac{-16-4\sqrt{7}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{7}}{2*3}=\frac{-16+4\sqrt{7}}{6}
$