F(x)=-x2-4x-3

Solution for F(x)=-x2-4x-3 equation:

(F)=-F2-4F-3

We move all terms to the left:

(F)-(-F2-4F-3)=0

We add all the numbers together, and all the variables

-(-1F^2-4F-3)+F=0

We get rid of parentheses

1F^2+4F+F+3=0

We add all the numbers together, and all the variables

F^2+5F+3=0

a = 1; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·1·3
Δ = 13
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{-(5)-\sqrt{13}}{2*1}=\frac{-5-\sqrt{13}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{13}}{2*1}=\frac{-5+\sqrt{13}}{2}
$