(50-2y/20)(400+y)=20240

Solution for (50-2y/20)(400+y)=20240 equation:

(50-2y/20)(400+y)=20240

We move all terms to the left:

(50-2y/20)(400+y)-(20240)=0


Domain of the equation: 20)(400+y)!=0

y∈R


We add all the numbers together, and all the variables

(-2y/20+50)(y+400)-20240=0

We multiply parentheses ..

(-2y^2-800y+50y+20000)-20240=0

We get rid of parentheses

-2y^2-800y+50y+20000-20240=0

We add all the numbers together, and all the variables

-2y^2-750y-240=0

a = -2; b = -750; c = -240;
Δ = b2-4ac
Δ = -7502-4·(-2)·(-240)
Δ = 560580
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{560580}=\sqrt{4*140145}=\sqrt{4}*\sqrt{140145}=2\sqrt{140145}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-750)-2\sqrt{140145}}{2*-2}=\frac{750-2\sqrt{140145}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-750)+2\sqrt{140145}}{2*-2}=\frac{750+2\sqrt{140145}}{-4}
$