17.86+21.98y(0.003746-y)=100-68.03y(1+y)

Solution for 17.86+21.98y(0.003746-y)=100-68.03y(1+y) equation:

17.86+21.98y(0.003746-y)=100-68.03y(1+y)

We move all terms to the left:

17.86+21.98y(0.003746-y)-(100-68.03y(1+y))=0

We add all the numbers together, and all the variables

21.98y(-1y+0.003746)-(100-68.03y(y+1))+17.86=0

We multiply parentheses

-21y^2+0.078666y-(100-68.03y(y+1))+17.86=0


We calculate terms in parentheses: -(100-68.03y(y+1)), so:

100-68.03y(y+1)

determiningTheFunctionDomain
-68.03y(y+1)+100

We multiply parentheses

-68y^2-68y+100

Back to the equation:

-(-68y^2-68y+100)


We get rid of parentheses

-21y^2+68y^2+68y+0.078666y-100+17.86=0

We add all the numbers together, and all the variables

47y^2+68.078666y-82.14=0

a = 47; b = 68.078666; c = -82.14;
Δ = b2-4ac
Δ = 68.0786662-4·47·(-82.14)
Δ = 20077.02476434
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{-(68.078666)-\sqrt{20077.02476434}}{2*47}=\frac{-68.078666-\sqrt{20077.02476434}}{94}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68.078666)+\sqrt{20077.02476434}}{2*47}=\frac{-68.078666+\sqrt{20077.02476434}}{94}
$