A=x(10-x)

Solution for A=x(10-x) equation:

=A(10-A)

We move all terms to the left:

-(A(10-A))=0

We add all the numbers together, and all the variables

-(A(-1A+10))=0


We calculate terms in parentheses: -(A(-1A+10)), so:

A(-1A+10)

We multiply parentheses

-1A^2+10A

Back to the equation:

-(-1A^2+10A)


We get rid of parentheses

1A^2-10A=0

We add all the numbers together, and all the variables

A^2-10A=0

a = 1; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·1·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*1}=\frac{0}{2}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*1}=\frac{20}{2}
=10
$