20.20+20.83y(0.003445-y)=100-68.97y(1+y)

Solution for 20.20+20.83y(0.003445-y)=100-68.97y(1+y) equation:

20.20+20.83y(0.003445-y)=100-68.97y(1+y)

We move all terms to the left:

20.20+20.83y(0.003445-y)-(100-68.97y(1+y))=0

We add all the numbers together, and all the variables

20.83y(-1y+0.003445)-(100-68.97y(y+1))+20.20=0

We add all the numbers together, and all the variables

20.83y(-1y+0.003445)-(100-68.97y(y+1))+20.2=0

We multiply parentheses

-20y^2+0.0689y-(100-68.97y(y+1))+20.2=0


We calculate terms in parentheses: -(100-68.97y(y+1)), so:

100-68.97y(y+1)

determiningTheFunctionDomain
-68.97y(y+1)+100

We multiply parentheses

-68y^2-68y+100

Back to the equation:

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


We get rid of parentheses

-20y^2+68y^2+68y+0.0689y-100+20.2=0

We add all the numbers together, and all the variables

48y^2+68.0689y-79.8=0

a = 48; b = 68.0689; c = -79.8;
Δ = b2-4ac
Δ = 68.06892-4·48·(-79.8)
Δ = 19954.97514721
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{-(68.0689)-\sqrt{19954.97514721}}{2*48}=\frac{-68.0689-\sqrt{19954.97514721}}{96}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68.0689)+\sqrt{19954.97514721}}{2*48}=\frac{-68.0689+\sqrt{19954.97514721}}{96}
$