F(x)=-3x^2-18x-15

Solution for F(x)=-3x^2-18x-15 equation:

(F)=-3F^2-18F-15

We move all terms to the left:

(F)-(-3F^2-18F-15)=0

We get rid of parentheses

3F^2+18F+F+15=0

We add all the numbers together, and all the variables

3F^2+19F+15=0

a = 3; b = 19; c = +15;
Δ = b2-4ac
Δ = 192-4·3·15
Δ = 181
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{-(19)-\sqrt{181}}{2*3}=\frac{-19-\sqrt{181}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{181}}{2*3}=\frac{-19+\sqrt{181}}{6}
$