16.39+20.83y(0.004128-y)=100-70.92y(1+y)

Solution for 16.39+20.83y(0.004128-y)=100-70.92y(1+y) equation:

16.39+20.83y(0.004128-y)=100-70.92y(1+y)

We move all terms to the left:

16.39+20.83y(0.004128-y)-(100-70.92y(1+y))=0

We add all the numbers together, and all the variables

20.83y(-1y+0.004128)-(100-70.92y(y+1))+16.39=0

We multiply parentheses

-20y^2+0.08256y-(100-70.92y(y+1))+16.39=0


We calculate terms in parentheses: -(100-70.92y(y+1)), so:

100-70.92y(y+1)

determiningTheFunctionDomain
-70.92y(y+1)+100

We multiply parentheses

-70y^2-70y+100

Back to the equation:

-(-70y^2-70y+100)


We get rid of parentheses

-20y^2+70y^2+70y+0.08256y-100+16.39=0

We add all the numbers together, and all the variables

50y^2+70.08256y-83.61=0

a = 50; b = 70.08256; c = -83.61;
Δ = b2-4ac
Δ = 70.082562-4·50·(-83.61)
Δ = 21633.565216154
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{-(70.08256)-\sqrt{21633.565216154}}{2*50}=\frac{-70.08256-\sqrt{21633.565216154}}{100}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70.08256)+\sqrt{21633.565216154}}{2*50}=\frac{-70.08256+\sqrt{21633.565216154}}{100}
$