14.49+21.05y(0.004523-y)=100-72.46y(1+y)

Solution for 14.49+21.05y(0.004523-y)=100-72.46y(1+y) equation:

14.49+21.05y(0.004523-y)=100-72.46y(1+y)

We move all terms to the left:

14.49+21.05y(0.004523-y)-(100-72.46y(1+y))=0

We add all the numbers together, and all the variables

21.05y(-1y+0.004523)-(100-72.46y(y+1))+14.49=0

We multiply parentheses

-21y^2+0.094983y-(100-72.46y(y+1))+14.49=0


We calculate terms in parentheses: -(100-72.46y(y+1)), so:

100-72.46y(y+1)

determiningTheFunctionDomain
-72.46y(y+1)+100

We multiply parentheses

-72y^2-72y+100

Back to the equation:

-(-72y^2-72y+100)


We get rid of parentheses

-21y^2+72y^2+72y+0.094983y-100+14.49=0

We add all the numbers together, and all the variables

51y^2+72.094983y-85.51=0

a = 51; b = 72.094983; c = -85.51;
Δ = b2-4ac
Δ = 72.0949832-4·51·(-85.51)
Δ = 22641.72657377
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{-(72.094983)-\sqrt{22641.72657377}}{2*51}=\frac{-72.094983-\sqrt{22641.72657377}}{102}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72.094983)+\sqrt{22641.72657377}}{2*51}=\frac{-72.094983+\sqrt{22641.72657377}}{102}
$