68.97+21.98y(0.003431-y)=100-19.23y(1+y)

Solution for 68.97+21.98y(0.003431-y)=100-19.23y(1+y) equation:

68.97+21.98y(0.003431-y)=100-19.23y(1+y)

We move all terms to the left:

68.97+21.98y(0.003431-y)-(100-19.23y(1+y))=0

We add all the numbers together, and all the variables

21.98y(-1y+0.003431)-(100-19.23y(y+1))+68.97=0

We multiply parentheses

-21y^2+0.072051y-(100-19.23y(y+1))+68.97=0


We calculate terms in parentheses: -(100-19.23y(y+1)), so:

100-19.23y(y+1)

determiningTheFunctionDomain
-19.23y(y+1)+100

We multiply parentheses

-19y^2-19y+100

Back to the equation:

-(-19y^2-19y+100)


We get rid of parentheses

-21y^2+19y^2+19y+0.072051y-100+68.97=0

We add all the numbers together, and all the variables

-2y^2+19.072051y-31.03=0

a = -2; b = 19.072051; c = -31.03;
Δ = b2-4ac
Δ = 19.0720512-4·(-2)·(-31.03)
Δ = 115.5031293466
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{-(19.072051)-\sqrt{115.5031293466}}{2*-2}=\frac{-19.072051-\sqrt{115.5031293466}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19.072051)+\sqrt{115.5031293466}}{2*-2}=\frac{-19.072051+\sqrt{115.5031293466}}{-4}
$