F(x)=-x^2-9x-4

Solution for F(x)=-x^2-9x-4 equation:

(F)=-F^2-9F-4

We move all terms to the left:

(F)-(-F^2-9F-4)=0

We get rid of parentheses

F^2+9F+F+4=0

We add all the numbers together, and all the variables

F^2+10F+4=0

a = 1; b = 10; c = +4;
Δ = b2-4ac
Δ = 102-4·1·4
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{21}}{2*1}=\frac{-10-2\sqrt{21}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{21}}{2*1}=\frac{-10+2\sqrt{21}}{2}
$