12.20+19.61y(0.005478-y)=100-76.34y(1+y)

Solution for 12.20+19.61y(0.005478-y)=100-76.34y(1+y) equation:

12.20+19.61y(0.005478-y)=100-76.34y(1+y)

We move all terms to the left:

12.20+19.61y(0.005478-y)-(100-76.34y(1+y))=0

We add all the numbers together, and all the variables

19.61y(-1y+0.005478)-(100-76.34y(y+1))+12.20=0

We add all the numbers together, and all the variables

19.61y(-1y+0.005478)-(100-76.34y(y+1))+12.2=0

We multiply parentheses

-19y^2+0.104082y-(100-76.34y(y+1))+12.2=0


We calculate terms in parentheses: -(100-76.34y(y+1)), so:

100-76.34y(y+1)

determiningTheFunctionDomain
-76.34y(y+1)+100

We multiply parentheses

-76y^2-76y+100

Back to the equation:

-(-76y^2-76y+100)


We get rid of parentheses

-19y^2+76y^2+76y+0.104082y-100+12.2=0

We add all the numbers together, and all the variables

57y^2+76.104082y-87.8=0

a = 57; b = 76.104082; c = -87.8;
Δ = b2-4ac
Δ = 76.1040822-4·57·(-87.8)
Δ = 25810.231297063
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{-(76.104082)-\sqrt{25810.231297063}}{2*57}=\frac{-76.104082-\sqrt{25810.231297063}}{114}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76.104082)+\sqrt{25810.231297063}}{2*57}=\frac{-76.104082+\sqrt{25810.231297063}}{114}
$