16.67+22.22y(0.004023-y)=100-67.11y(1+y)

Solution for 16.67+22.22y(0.004023-y)=100-67.11y(1+y) equation:

16.67+22.22y(0.004023-y)=100-67.11y(1+y)

We move all terms to the left:

16.67+22.22y(0.004023-y)-(100-67.11y(1+y))=0

We add all the numbers together, and all the variables

22.22y(-1y+0.004023)-(100-67.11y(y+1))+16.67=0

We multiply parentheses

-22y^2+0.088506y-(100-67.11y(y+1))+16.67=0


We calculate terms in parentheses: -(100-67.11y(y+1)), so:

100-67.11y(y+1)

determiningTheFunctionDomain
-67.11y(y+1)+100

We multiply parentheses

-67y^2-67y+100

Back to the equation:

-(-67y^2-67y+100)


We get rid of parentheses

-22y^2+67y^2+67y+0.088506y-100+16.67=0

We add all the numbers together, and all the variables

45y^2+67.088506y-83.33=0

a = 45; b = 67.088506; c = -83.33;
Δ = b2-4ac
Δ = 67.0885062-4·45·(-83.33)
Δ = 19500.267637312
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{-(67.088506)-\sqrt{19500.267637312}}{2*45}=\frac{-67.088506-\sqrt{19500.267637312}}{90}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(67.088506)+\sqrt{19500.267637312}}{2*45}=\frac{-67.088506+\sqrt{19500.267637312}}{90}
$