Y=x(50-x)

Solution for Y=x(50-x) equation:

=Y(50-Y)

We move all terms to the left:

-(Y(50-Y))=0

We add all the numbers together, and all the variables

-(Y(-1Y+50))=0


We calculate terms in parentheses: -(Y(-1Y+50)), so:

Y(-1Y+50)

We multiply parentheses

-1Y^2+50Y

Back to the equation:

-(-1Y^2+50Y)


We get rid of parentheses

1Y^2-50Y=0

We add all the numbers together, and all the variables

Y^2-50Y=0

a = 1; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·1·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*1}=\frac{0}{2}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*1}=\frac{100}{2}
=50
$