Y=x(15000-75x)

Solution for Y=x(15000-75x) equation:

=Y(15000-75Y)

We move all terms to the left:

-(Y(15000-75Y))=0

We add all the numbers together, and all the variables

-(Y(-75Y+15000))=0


We calculate terms in parentheses: -(Y(-75Y+15000)), so:

Y(-75Y+15000)

We multiply parentheses

-75Y^2+15000Y

Back to the equation:

-(-75Y^2+15000Y)


We get rid of parentheses

75Y^2-15000Y=0

a = 75; b = -15000; c = 0;
Δ = b2-4ac
Δ = -150002-4·75·0
Δ = 225000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225000000}=15000$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15000)-15000}{2*75}=\frac{0}{150}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15000)+15000}{2*75}=\frac{30000}{150}
=200
$