A(x)=20x-0,5x2

Solution for A(x)=20x-0,5x2 equation:

(A)=20A-0.5A^2

We move all terms to the left:

(A)-(20A-0.5A^2)=0

We get rid of parentheses

0.5A^2-20A+A=0

We add all the numbers together, and all the variables

0.5A^2-19A=0

a = 0.5; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·0.5·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*0.5}=\frac{0}{1}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*0.5}=\frac{38}{1}
=38
$