A=2y(5-y)

Solution for A=2y(5-y) equation:

=2A(5-A)

We move all terms to the left:

-(2A(5-A))=0

We add all the numbers together, and all the variables

-(2A(-1A+5))=0


We calculate terms in parentheses: -(2A(-1A+5)), so:

2A(-1A+5)

We multiply parentheses

-2A^2+10A

Back to the equation:

-(-2A^2+10A)


We get rid of parentheses

2A^2-10A=0

a = 2; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·2·0
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*2}=\frac{0}{4}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*2}=\frac{20}{4}
=5
$