21.51+22.99y(0.003095-y)=100-65.36y(1+y)

Solution for 21.51+22.99y(0.003095-y)=100-65.36y(1+y) equation:

21.51+22.99y(0.003095-y)=100-65.36y(1+y)

We move all terms to the left:

21.51+22.99y(0.003095-y)-(100-65.36y(1+y))=0

We add all the numbers together, and all the variables

22.99y(-1y+0.003095)-(100-65.36y(y+1))+21.51=0

We multiply parentheses

-22y^2+0.06809y-(100-65.36y(y+1))+21.51=0


We calculate terms in parentheses: -(100-65.36y(y+1)), so:

100-65.36y(y+1)

determiningTheFunctionDomain
-65.36y(y+1)+100

We multiply parentheses

-65y^2-65y+100

Back to the equation:

-(-65y^2-65y+100)


We get rid of parentheses

-22y^2+65y^2+65y+0.06809y-100+21.51=0

We add all the numbers together, and all the variables

43y^2+65.06809y-78.49=0

a = 43; b = 65.06809; c = -78.49;
Δ = b2-4ac
Δ = 65.068092-4·43·(-78.49)
Δ = 17734.136336248
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{-(65.06809)-\sqrt{17734.136336248}}{2*43}=\frac{-65.06809-\sqrt{17734.136336248}}{86}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65.06809)+\sqrt{17734.136336248}}{2*43}=\frac{-65.06809+\sqrt{17734.136336248}}{86}
$