17.24+22.99y(0.003709-y)=100-68.03y(1+y)

Solution for 17.24+22.99y(0.003709-y)=100-68.03y(1+y) equation:

17.24+22.99y(0.003709-y)=100-68.03y(1+y)

We move all terms to the left:

17.24+22.99y(0.003709-y)-(100-68.03y(1+y))=0

We add all the numbers together, and all the variables

22.99y(-1y+0.003709)-(100-68.03y(y+1))+17.24=0

We multiply parentheses

-22y^2+0.081598y-(100-68.03y(y+1))+17.24=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

-22y^2+68y^2+68y+0.081598y-100+17.24=0

We add all the numbers together, and all the variables

46y^2+68.081598y-82.76=0

a = 46; b = 68.081598; c = -82.76;
Δ = b2-4ac
Δ = 68.0815982-4·46·(-82.76)
Δ = 19862.943986234
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{-(68.081598)-\sqrt{19862.943986234}}{2*46}=\frac{-68.081598-\sqrt{19862.943986234}}{92}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68.081598)+\sqrt{19862.943986234}}{2*46}=\frac{-68.081598+\sqrt{19862.943986234}}{92}
$