9.76+17.24y(0.007193-y)=100-82.64y(1+y)

Solution for 9.76+17.24y(0.007193-y)=100-82.64y(1+y) equation:

9.76+17.24y(0.007193-y)=100-82.64y(1+y)

We move all terms to the left:

9.76+17.24y(0.007193-y)-(100-82.64y(1+y))=0

We add all the numbers together, and all the variables

17.24y(-1y+0.007193)-(100-82.64y(y+1))+9.76=0

We multiply parentheses

-17y^2+0.122281y-(100-82.64y(y+1))+9.76=0


We calculate terms in parentheses: -(100-82.64y(y+1)), so:

100-82.64y(y+1)

determiningTheFunctionDomain
-82.64y(y+1)+100

We multiply parentheses

-82y^2-82y+100

Back to the equation:

-(-82y^2-82y+100)


We get rid of parentheses

-17y^2+82y^2+82y+0.122281y-100+9.76=0

We add all the numbers together, and all the variables

65y^2+82.122281y-90.24=0

a = 65; b = 82.122281; c = -90.24;
Δ = b2-4ac
Δ = 82.1222812-4·65·(-90.24)
Δ = 30206.469036643
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{-(82.122281)-\sqrt{30206.469036643}}{2*65}=\frac{-82.122281-\sqrt{30206.469036643}}{130}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82.122281)+\sqrt{30206.469036643}}{2*65}=\frac{-82.122281+\sqrt{30206.469036643}}{130}
$