14.93+19.61y(0.00451-y)=100-75.76y(1+y)

Solution for 14.93+19.61y(0.00451-y)=100-75.76y(1+y) equation:

14.93+19.61y(0.00451-y)=100-75.76y(1+y)

We move all terms to the left:

14.93+19.61y(0.00451-y)-(100-75.76y(1+y))=0

We add all the numbers together, and all the variables

19.61y(-1y+0.00451)-(100-75.76y(y+1))+14.93=0

We multiply parentheses

-19y^2+0.08569y-(100-75.76y(y+1))+14.93=0


We calculate terms in parentheses: -(100-75.76y(y+1)), so:

100-75.76y(y+1)

determiningTheFunctionDomain
-75.76y(y+1)+100

We multiply parentheses

-75y^2-75y+100

Back to the equation:

-(-75y^2-75y+100)


We get rid of parentheses

-19y^2+75y^2+75y+0.08569y-100+14.93=0

We add all the numbers together, and all the variables

56y^2+75.08569y-85.07=0

a = 56; b = 75.08569; c = -85.07;
Δ = b2-4ac
Δ = 75.085692-4·56·(-85.07)
Δ = 24693.540842776
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{-(75.08569)-\sqrt{24693.540842776}}{2*56}=\frac{-75.08569-\sqrt{24693.540842776}}{112}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75.08569)+\sqrt{24693.540842776}}{2*56}=\frac{-75.08569+\sqrt{24693.540842776}}{112}
$