F(x)=20x+x^2

Solution for F(x)=20x+x^2 equation:

(F)=20F+F^2

We move all terms to the left:

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

We get rid of parentheses

-F^2-20F+F=0

We add all the numbers together, and all the variables

-1F^2-19F=0

a = -1; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·(-1)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*-1}=\frac{0}{-2}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*-1}=\frac{38}{-2}
=-19
$