Y=0.3x(24-x)

Solution for Y=0.3x(24-x) equation:

=0.3Y(24-Y)

We move all terms to the left:

-(0.3Y(24-Y))=0

We add all the numbers together, and all the variables

-(0.3Y(-1Y+24))=0


We calculate terms in parentheses: -(0.3Y(-1Y+24)), so:

0.3Y(-1Y+24)

We multiply parentheses

0Y^2+0Y

We add all the numbers together, and all the variables

Y^2+Y

Back to the equation:

-(Y^2+Y)


We get rid of parentheses

-Y^2-Y=0

We add all the numbers together, and all the variables

-1Y^2-1Y=0

a = -1; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-1)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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