16.13+20y(0.004185-y)=100-74.07y(1+y)

Solution for 16.13+20y(0.004185-y)=100-74.07y(1+y) equation:

16.13+20y(0.004185-y)=100-74.07y(1+y)

We move all terms to the left:

16.13+20y(0.004185-y)-(100-74.07y(1+y))=0

We add all the numbers together, and all the variables

20y(-1y+0.004185)-(100-74.07y(y+1))+16.13=0

We multiply parentheses

-20y^2+0.0837y-(100-74.07y(y+1))+16.13=0


We calculate terms in parentheses: -(100-74.07y(y+1)), so:

100-74.07y(y+1)

determiningTheFunctionDomain
-74.07y(y+1)+100

We multiply parentheses

-74y^2-74y+100

Back to the equation:

-(-74y^2-74y+100)


We get rid of parentheses

-20y^2+74y^2+74y+0.0837y-100+16.13=0

We add all the numbers together, and all the variables

54y^2+74.0837y-83.87=0

a = 54; b = 74.0837; c = -83.87;
Δ = b2-4ac
Δ = 74.08372-4·54·(-83.87)
Δ = 23604.31460569
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{-(74.0837)-\sqrt{23604.31460569}}{2*54}=\frac{-74.0837-\sqrt{23604.31460569}}{108}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(74.0837)+\sqrt{23604.31460569}}{2*54}=\frac{-74.0837+\sqrt{23604.31460569}}{108}
$