17.24+22.22y(0.003811-y)=100-68.49y(1+y)

Solution for 17.24+22.22y(0.003811-y)=100-68.49y(1+y) equation:

17.24+22.22y(0.003811-y)=100-68.49y(1+y)

We move all terms to the left:

17.24+22.22y(0.003811-y)-(100-68.49y(1+y))=0

We add all the numbers together, and all the variables

22.22y(-1y+0.003811)-(100-68.49y(y+1))+17.24=0

We multiply parentheses

-22y^2+0.083842y-(100-68.49y(y+1))+17.24=0


We calculate terms in parentheses: -(100-68.49y(y+1)), so:

100-68.49y(y+1)

determiningTheFunctionDomain
-68.49y(y+1)+100

We multiply parentheses

-68y^2-68y+100

Back to the equation:

-(-68y^2-68y+100)


We get rid of parentheses

-22y^2+68y^2+68y+0.083842y-100+17.24=0

We add all the numbers together, and all the variables

46y^2+68.083842y-82.76=0

a = 46; b = 68.083842; c = -82.76;
Δ = b2-4ac
Δ = 68.0838422-4·46·(-82.76)
Δ = 19863.249541481
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{-(68.083842)-\sqrt{19863.249541481}}{2*46}=\frac{-68.083842-\sqrt{19863.249541481}}{92}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68.083842)+\sqrt{19863.249541481}}{2*46}=\frac{-68.083842+\sqrt{19863.249541481}}{92}
$