Y=-50(x^2+75x)+125000

Solution for Y=-50(x^2+75x)+125000 equation:

=-50(Y^2+75Y)+125000

We move all terms to the left:

-(-50(Y^2+75Y)+125000)=0


We calculate terms in parentheses: -(-50(Y^2+75Y)+125000), so:

-50(Y^2+75Y)+125000

We multiply parentheses

-50Y^2-3750Y+125000

Back to the equation:

-(-50Y^2-3750Y+125000)


We get rid of parentheses

50Y^2+3750Y-125000=0

a = 50; b = 3750; c = -125000;
Δ = b2-4ac
Δ = 37502-4·50·(-125000)
Δ = 39062500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39062500}=6250$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3750)-6250}{2*50}=\frac{-10000}{100}
=-100
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3750)+6250}{2*50}=\frac{2500}{100}
=25
$