11.63+17.86y(0.006116-y)=100-78.74y(1+y)

Solution for 11.63+17.86y(0.006116-y)=100-78.74y(1+y) equation:

11.63+17.86y(0.006116-y)=100-78.74y(1+y)

We move all terms to the left:

11.63+17.86y(0.006116-y)-(100-78.74y(1+y))=0

We add all the numbers together, and all the variables

17.86y(-1y+0.006116)-(100-78.74y(y+1))+11.63=0

We multiply parentheses

-17y^2+0.103972y-(100-78.74y(y+1))+11.63=0


We calculate terms in parentheses: -(100-78.74y(y+1)), so:

100-78.74y(y+1)

determiningTheFunctionDomain
-78.74y(y+1)+100

We multiply parentheses

-78y^2-78y+100

Back to the equation:

-(-78y^2-78y+100)


We get rid of parentheses

-17y^2+78y^2+78y+0.103972y-100+11.63=0

We add all the numbers together, and all the variables

61y^2+78.103972y-88.37=0

a = 61; b = 78.103972; c = -88.37;
Δ = b2-4ac
Δ = 78.1039722-4·61·(-88.37)
Δ = 27662.510442177
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{-(78.103972)-\sqrt{27662.510442177}}{2*61}=\frac{-78.103972-\sqrt{27662.510442177}}{122}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78.103972)+\sqrt{27662.510442177}}{2*61}=\frac{-78.103972+\sqrt{27662.510442177}}{122}
$