12.35+21.51y(0.005537-y)=100-68.03y(1+y)

Solution for 12.35+21.51y(0.005537-y)=100-68.03y(1+y) equation:

12.35+21.51y(0.005537-y)=100-68.03y(1+y)

We move all terms to the left:

12.35+21.51y(0.005537-y)-(100-68.03y(1+y))=0

We add all the numbers together, and all the variables

21.51y(-1y+0.005537)-(100-68.03y(y+1))+12.35=0

We multiply parentheses

-21y^2+0.116277y-(100-68.03y(y+1))+12.35=0


We calculate terms in parentheses: -(100-68.03y(y+1)), so:

100-68.03y(y+1)

determiningTheFunctionDomain
-68.03y(y+1)+100

We multiply parentheses

-68y^2-68y+100

Back to the equation:

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


We get rid of parentheses

-21y^2+68y^2+68y+0.116277y-100+12.35=0

We add all the numbers together, and all the variables

47y^2+68.116277y-87.65=0

a = 47; b = 68.116277; c = -87.65;
Δ = b2-4ac
Δ = 68.1162772-4·47·(-87.65)
Δ = 21118.027192341
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{-(68.116277)-\sqrt{21118.027192341}}{2*47}=\frac{-68.116277-\sqrt{21118.027192341}}{94}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68.116277)+\sqrt{21118.027192341}}{2*47}=\frac{-68.116277+\sqrt{21118.027192341}}{94}
$