14.93+23.53y(0.0041-y)=100-69.44y(1+y)

Solution for 14.93+23.53y(0.0041-y)=100-69.44y(1+y) equation:

14.93+23.53y(0.0041-y)=100-69.44y(1+y)

We move all terms to the left:

14.93+23.53y(0.0041-y)-(100-69.44y(1+y))=0

We add all the numbers together, and all the variables

23.53y(-1y+0.0041)-(100-69.44y(y+1))+14.93=0

We multiply parentheses

-23y^2+0.0943y-(100-69.44y(y+1))+14.93=0


We calculate terms in parentheses: -(100-69.44y(y+1)), so:

100-69.44y(y+1)

determiningTheFunctionDomain
-69.44y(y+1)+100

We multiply parentheses

-69y^2-69y+100

Back to the equation:

-(-69y^2-69y+100)


We get rid of parentheses

-23y^2+69y^2+69y+0.0943y-100+14.93=0

We add all the numbers together, and all the variables

46y^2+69.0943y-85.07=0

a = 46; b = 69.0943; c = -85.07;
Δ = b2-4ac
Δ = 69.09432-4·46·(-85.07)
Δ = 20426.90229249
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{-(69.0943)-\sqrt{20426.90229249}}{2*46}=\frac{-69.0943-\sqrt{20426.90229249}}{92}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69.0943)+\sqrt{20426.90229249}}{2*46}=\frac{-69.0943+\sqrt{20426.90229249}}{92}
$