A=13x-x^2

Solution for A=13x-x^2 equation:

=13A-A^2

We move all terms to the left:

-(13A-A^2)=0

We get rid of parentheses

A^2-13A=0

a = 1; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·1·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*1}=\frac{0}{2}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*1}=\frac{26}{2}
=13
$