14.71+21.74y(0.004254-y)=100-73.53y(1+y)

Solution for 14.71+21.74y(0.004254-y)=100-73.53y(1+y) equation:

14.71+21.74y(0.004254-y)=100-73.53y(1+y)

We move all terms to the left:

14.71+21.74y(0.004254-y)-(100-73.53y(1+y))=0

We add all the numbers together, and all the variables

21.74y(-1y+0.004254)-(100-73.53y(y+1))+14.71=0

We multiply parentheses

-21y^2+0.089334y-(100-73.53y(y+1))+14.71=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

-21y^2+73y^2+73y+0.089334y-100+14.71=0

We add all the numbers together, and all the variables

52y^2+73.089334y-85.29=0

a = 52; b = 73.089334; c = -85.29;
Δ = b2-4ac
Δ = 73.0893342-4·52·(-85.29)
Δ = 23082.370744564
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{-(73.089334)-\sqrt{23082.370744564}}{2*52}=\frac{-73.089334-\sqrt{23082.370744564}}{104}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(73.089334)+\sqrt{23082.370744564}}{2*52}=\frac{-73.089334+\sqrt{23082.370744564}}{104}
$