F(x)=-x^2-14x-47

Solution for F(x)=-x^2-14x-47 equation:

(F)=-F^2-14F-47

We move all terms to the left:

(F)-(-F^2-14F-47)=0

We get rid of parentheses

F^2+14F+F+47=0

We add all the numbers together, and all the variables

F^2+15F+47=0

a = 1; b = 15; c = +47;
Δ = b2-4ac
Δ = 152-4·1·47
Δ = 37
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{-(15)-\sqrt{37}}{2*1}=\frac{-15-\sqrt{37}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{37}}{2*1}=\frac{-15+\sqrt{37}}{2}
$