13.89+20y(0.00486-y)=100-74.07y(1+y)

Solution for 13.89+20y(0.00486-y)=100-74.07y(1+y) equation:

13.89+20y(0.00486-y)=100-74.07y(1+y)

We move all terms to the left:

13.89+20y(0.00486-y)-(100-74.07y(1+y))=0

We add all the numbers together, and all the variables

20y(-1y+0.00486)-(100-74.07y(y+1))+13.89=0

We multiply parentheses

-20y^2+0.0972y-(100-74.07y(y+1))+13.89=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+0.0972y-100+13.89=0

We add all the numbers together, and all the variables

54y^2+74.0972y-86.11=0

a = 54; b = 74.0972; c = -86.11;
Δ = b2-4ac
Δ = 74.09722-4·54·(-86.11)
Δ = 24090.15504784
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{-(74.0972)-\sqrt{24090.15504784}}{2*54}=\frac{-74.0972-\sqrt{24090.15504784}}{108}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(74.0972)+\sqrt{24090.15504784}}{2*54}=\frac{-74.0972+\sqrt{24090.15504784}}{108}
$