12.66+19.61y(0.005318-y)=100-75.76y(1+y)

Solution for 12.66+19.61y(0.005318-y)=100-75.76y(1+y) equation:

12.66+19.61y(0.005318-y)=100-75.76y(1+y)

We move all terms to the left:

12.66+19.61y(0.005318-y)-(100-75.76y(1+y))=0

We add all the numbers together, and all the variables

19.61y(-1y+0.005318)-(100-75.76y(y+1))+12.66=0

We multiply parentheses

-19y^2+0.101042y-(100-75.76y(y+1))+12.66=0


We calculate terms in parentheses: -(100-75.76y(y+1)), so:

100-75.76y(y+1)

determiningTheFunctionDomain
-75.76y(y+1)+100

We multiply parentheses

-75y^2-75y+100

Back to the equation:

-(-75y^2-75y+100)


We get rid of parentheses

-19y^2+75y^2+75y+0.101042y-100+12.66=0

We add all the numbers together, and all the variables

56y^2+75.101042y-87.34=0

a = 56; b = 75.101042; c = -87.34;
Δ = b2-4ac
Δ = 75.1010422-4·56·(-87.34)
Δ = 25204.326509486
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{-(75.101042)-\sqrt{25204.326509486}}{2*56}=\frac{-75.101042-\sqrt{25204.326509486}}{112}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75.101042)+\sqrt{25204.326509486}}{2*56}=\frac{-75.101042+\sqrt{25204.326509486}}{112}
$