15.38+20.20y(0.004344-y)=100-74.07y(1+y)

Solution for 15.38+20.20y(0.004344-y)=100-74.07y(1+y) equation:

15.38+20.20y(0.004344-y)=100-74.07y(1+y)

We move all terms to the left:

15.38+20.20y(0.004344-y)-(100-74.07y(1+y))=0

We add all the numbers together, and all the variables

20.20y(-1y+0.004344)-(100-74.07y(y+1))+15.38=0

We multiply parentheses

-20y^2+0.08688y-(100-74.07y(y+1))+15.38=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+0.08688y-100+15.38=0

We add all the numbers together, and all the variables

54y^2+74.08688y-84.62=0

a = 54; b = 74.08688; c = -84.62;
Δ = b2-4ac
Δ = 74.086882-4·54·(-84.62)
Δ = 23766.785788134
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{-(74.08688)-\sqrt{23766.785788134}}{2*54}=\frac{-74.08688-\sqrt{23766.785788134}}{108}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(74.08688)+\sqrt{23766.785788134}}{2*54}=\frac{-74.08688+\sqrt{23766.785788134}}{108}
$