44.4+29.9y(0.00214-y)=100-35.1y(1+y)

Solution for 44.4+29.9y(0.00214-y)=100-35.1y(1+y) equation:

44.4+29.9y(0.00214-y)=100-35.1y(1+y)

We move all terms to the left:

44.4+29.9y(0.00214-y)-(100-35.1y(1+y))=0

We add all the numbers together, and all the variables

29.9y(-1y+0.00214)-(100-35.1y(y+1))+44.4=0

We multiply parentheses

-29y^2+0.06206y-(100-35.1y(y+1))+44.4=0


We calculate terms in parentheses: -(100-35.1y(y+1)), so:

100-35.1y(y+1)

determiningTheFunctionDomain
-35.1y(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+0.06206y-100+44.4=0

We add all the numbers together, and all the variables

6y^2+35.06206y-55.6=0

a = 6; b = 35.06206; c = -55.6;
Δ = b2-4ac
Δ = 35.062062-4·6·(-55.6)
Δ = 2563.7480514436
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{-(35.06206)-\sqrt{2563.7480514436}}{2*6}=\frac{-35.06206-\sqrt{2563.7480514436}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35.06206)+\sqrt{2563.7480514436}}{2*6}=\frac{-35.06206+\sqrt{2563.7480514436}}{12}
$