Y=4x(10-x)

Solution for Y=4x(10-x) equation:

=4Y(10-Y)

We move all terms to the left:

-(4Y(10-Y))=0

We add all the numbers together, and all the variables

-(4Y(-1Y+10))=0


We calculate terms in parentheses: -(4Y(-1Y+10)), so:

4Y(-1Y+10)

We multiply parentheses

-4Y^2+40Y

Back to the equation:

-(-4Y^2+40Y)


We get rid of parentheses

4Y^2-40Y=0

a = 4; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·4·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*4}=\frac{0}{8}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*4}=\frac{80}{8}
=10
$