11.24+16.39y(0.006732-y)=100-80.65y(1+y)

Solution for 11.24+16.39y(0.006732-y)=100-80.65y(1+y) equation:

11.24+16.39y(0.006732-y)=100-80.65y(1+y)

We move all terms to the left:

11.24+16.39y(0.006732-y)-(100-80.65y(1+y))=0

We add all the numbers together, and all the variables

16.39y(-1y+0.006732)-(100-80.65y(y+1))+11.24=0

We multiply parentheses

-16y^2+0.107712y-(100-80.65y(y+1))+11.24=0


We calculate terms in parentheses: -(100-80.65y(y+1)), so:

100-80.65y(y+1)

determiningTheFunctionDomain
-80.65y(y+1)+100

We multiply parentheses

-80y^2-80y+100

Back to the equation:

-(-80y^2-80y+100)


We get rid of parentheses

-16y^2+80y^2+80y+0.107712y-100+11.24=0

We add all the numbers together, and all the variables

64y^2+80.107712y-88.76=0

a = 64; b = 80.107712; c = -88.76;
Δ = b2-4ac
Δ = 80.1077122-4·64·(-88.76)
Δ = 29139.805521875
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{-(80.107712)-\sqrt{29139.805521875}}{2*64}=\frac{-80.107712-\sqrt{29139.805521875}}{128}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80.107712)+\sqrt{29139.805521875}}{2*64}=\frac{-80.107712+\sqrt{29139.805521875}}{128}
$