Y=(20-0.5x)(3000+125x)

Solution for Y=(20-0.5x)(3000+125x) equation:

=(20-0.5Y)(3000+125Y)

We move all terms to the left:

-((20-0.5Y)(3000+125Y))=0

We add all the numbers together, and all the variables

-((-0.5Y+20)(125Y+3000))=0

We multiply parentheses ..

-((+0Y^2+0Y+2500Y+60000))=0


We calculate terms in parentheses: -((+0Y^2+0Y+2500Y+60000)), so:

(+0Y^2+0Y+2500Y+60000)

We get rid of parentheses

0Y^2+0Y+2500Y+60000

We add all the numbers together, and all the variables

Y^2+2501Y+60000

Back to the equation:

-(Y^2+2501Y+60000)


We get rid of parentheses

-Y^2-2501Y-60000=0

We add all the numbers together, and all the variables

-1Y^2-2501Y-60000=0

a = -1; b = -2501; c = -60000;
Δ = b2-4ac
Δ = -25012-4·(-1)·(-60000)
Δ = 6015001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2501)-\sqrt{6015001}}{2*-1}=\frac{2501-\sqrt{6015001}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2501)+\sqrt{6015001}}{2*-1}=\frac{2501+\sqrt{6015001}}{-2}
$