44.44+29.85y(0.002111-y)=100-35.71y(1+y)

Solution for 44.44+29.85y(0.002111-y)=100-35.71y(1+y) equation:

44.44+29.85y(0.002111-y)=100-35.71y(1+y)

We move all terms to the left:

44.44+29.85y(0.002111-y)-(100-35.71y(1+y))=0

We add all the numbers together, and all the variables

29.85y(-1y+0.002111)-(100-35.71y(y+1))+44.44=0

We multiply parentheses

-29y^2+0.061219y-(100-35.71y(y+1))+44.44=0


We calculate terms in parentheses: -(100-35.71y(y+1)), so:

100-35.71y(y+1)

determiningTheFunctionDomain
-35.71y(y+1)+100

We multiply parentheses

-35y^2-35y+100

Back to the equation:

-(-35y^2-35y+100)


We get rid of parentheses

-29y^2+35y^2+35y+0.061219y-100+44.44=0

We add all the numbers together, and all the variables

6y^2+35.061219y-55.56=0

a = 6; b = 35.061219; c = -55.56;
Δ = b2-4ac
Δ = 35.0612192-4·6·(-55.56)
Δ = 2562.729077766
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{-(35.061219)-\sqrt{2562.729077766}}{2*6}=\frac{-35.061219-\sqrt{2562.729077766}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35.061219)+\sqrt{2562.729077766}}{2*6}=\frac{-35.061219+\sqrt{2562.729077766}}{12}
$