10.2+18.18y(0.00733-y)=100-73.53y(1+y)

Solution for 10.2+18.18y(0.00733-y)=100-73.53y(1+y) equation:

10.2+18.18y(0.00733-y)=100-73.53y(1+y)

We move all terms to the left:

10.2+18.18y(0.00733-y)-(100-73.53y(1+y))=0

We add all the numbers together, and all the variables

18.18y(-1y+0.00733)-(100-73.53y(y+1))+10.2=0

We multiply parentheses

-18y^2+0.13194y-(100-73.53y(y+1))+10.2=0


We calculate terms in parentheses: -(100-73.53y(y+1)), so:

100-73.53y(y+1)

determiningTheFunctionDomain
-73.53y(y+1)+100

We multiply parentheses

-73y^2-73y+100

Back to the equation:

-(-73y^2-73y+100)


We get rid of parentheses

-18y^2+73y^2+73y+0.13194y-100+10.2=0

We add all the numbers together, and all the variables

55y^2+73.13194y-89.8=0

a = 55; b = 73.13194; c = -89.8;
Δ = b2-4ac
Δ = 73.131942-4·55·(-89.8)
Δ = 25104.280648164
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{-(73.13194)-\sqrt{25104.280648164}}{2*55}=\frac{-73.13194-\sqrt{25104.280648164}}{110}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(73.13194)+\sqrt{25104.280648164}}{2*55}=\frac{-73.13194+\sqrt{25104.280648164}}{110}
$