A=x(x+8)=256

Solution for A=x(x+8)=256 equation:

=A(A+8)=256

We move all terms to the left:

-(A(A+8))=0


We calculate terms in parentheses: -(A(A+8)), so:

A(A+8)

We multiply parentheses

A^2+8A

Back to the equation:

-(A^2+8A)


We get rid of parentheses

-A^2-8A=0

We add all the numbers together, and all the variables

-1A^2-8A=0

a = -1; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-1)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-1}=\frac{0}{-2}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-1}=\frac{16}{-2}
=-8
$