F(x)=-x2+4x+20

Solution for F(x)=-x2+4x+20 equation:

(F)=-F2+4F+20

We move all terms to the left:

(F)-(-F2+4F+20)=0

We add all the numbers together, and all the variables

-(-1F^2+4F+20)+F=0

We get rid of parentheses

1F^2-4F+F-20=0

We add all the numbers together, and all the variables

F^2-3F-20=0

a = 1; b = -3; c = -20;
Δ = b2-4ac
Δ = -32-4·1·(-20)
Δ = 89
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{-(-3)-\sqrt{89}}{2*1}=\frac{3-\sqrt{89}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{89}}{2*1}=\frac{3+\sqrt{89}}{2}
$