Y=(20x+1)(700-25x)

Solution for Y=(20x+1)(700-25x) equation:

=(20Y+1)(700-25Y)

We move all terms to the left:

-((20Y+1)(700-25Y))=0

We add all the numbers together, and all the variables

-((20Y+1)(-25Y+700))=0

We multiply parentheses ..

-((-500Y^2+14000Y-25Y+700))=0


We calculate terms in parentheses: -((-500Y^2+14000Y-25Y+700)), so:

(-500Y^2+14000Y-25Y+700)

We get rid of parentheses

-500Y^2+14000Y-25Y+700

We add all the numbers together, and all the variables

-500Y^2+13975Y+700

Back to the equation:

-(-500Y^2+13975Y+700)


We get rid of parentheses

500Y^2-13975Y-700=0

a = 500; b = -13975; c = -700;
Δ = b2-4ac
Δ = -139752-4·500·(-700)
Δ = 196700625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196700625}=14025$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13975)-14025}{2*500}=\frac{-50}{1000}
=-1/20
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13975)+14025}{2*500}=\frac{28000}{1000}
=28
$